All roses are flowers. All flowers are plants. Which conclusion must be true?

Correct: C) All roses are plants.

Transitive inclusion: rose ⊆ flower ⊆ plant, so every rose is a plant (C). A reverses the relation, B contradicts the premise, and D over-restricts — none is guaranteed.

“If you flip the switch, the fan spins.” You flipped the switch. What must be true?

Correct: B) The fan spins.

This is affirming the antecedent (modus ponens): the antecedent 'flipped' holds, so the consequent 'spins' must follow (B). C affirms the consequent, an invalid direction that is not guaranteed.

A river is longer than a pool. A pool is longer than a pond. Which must be true?

Correct: A) The river is longer than the pond.

'Longer than' is transitive: river > pool > pond, so river > pond (A). C reverses it, B is wrong since the river is longest, and D has no basis in the premises.

What is the logical negation of “All the books on this shelf are new”?

Correct: D) At least one book is not new.

The negation of 'all are new' is 'at least one is not new' (D). A and B state the contrary (none is new), not the negation, and C is consistent with the original claim, so it does not negate it.

All surgeons are careful. Some lecturers are surgeons. Which must be true?

Correct: B) Some lecturers are careful.

Some lecturers are surgeons, and surgeons are careful, so some lecturers are careful (B). A over-strengthens to 'all', C reverses the relation, and D contradicts the premises — all exceed what is guaranteed.

“If you pour water, the seed sprouts.” The seed did not sprout. What must be true?

Correct: A) Water was not poured.

Contrapositive: 'did not sprout' implies 'water not poured'. Had water been poured, it would have sprouted; since it did not, water was not poured (A). C guesses at a cause not in the premises, so it is not guaranteed.

Lin is faster than Mei. Noah is faster than Lin. Mei is faster than Kei. Who is the fastest?

Correct: D) Noah

Noah > Lin > Mei and Mei > Kei, so overall Noah > Lin > Mei > Kei. The fastest is Noah (D). Kei is the slowest, so C is wrong.

What is the logical negation of “Some products are on sale”?

Correct: A) No product is on sale.

'Some are (at least one exists)' is negated by 'none are (all are not)' (A). B merely says some others are not, which is compatible with the original, and D is the same; C moves in the wrong direction.

All conductors carry current. Wood does not carry current. Which must be true?

Correct: C) Wood is not a conductor.

This uses the contrapositive: 'conductor → carries current' gives 'does not carry current → not a conductor'. Wood does not carry current, so wood is not a conductor (C). B is the converse and fails because non-conductors can also carry current.

“If you pass the interview, you get an offer. If you get an offer, you can join.” Rei passed the interview. What must be true?

Correct: D) Rei can join.

Chain the conditionals: pass → offer → can join, so Rei can join (D). A and B guess at choices not in the premises and are not guaranteed.

Five books sit left to right on a shelf. Blue is immediately to the right of Red. Green is somewhere to the left of Red. Yellow is immediately to the right of Blue. Which ordering statement must be true? (left to right)

Correct: B) Green is always to the left of Blue.

The fixed block is Green … Red, Blue, Yellow (Blue right of Red, Yellow right of Blue, Green left of Red), so Green is left of Blue (B). Another book could sit right of Yellow, so A is unsettled; one could sit left of Green, so C is unsettled; a book could sit between Red and Green, so D is unsettled too.

It turns out that “everyone on this team is good at both planning and execution” is false. Which must be true?

Correct: D) At least one person is bad at planning or bad at execution (at least one of the two).

Negating 'everyone is good at (planning AND execution)' gives 'at least one person is not good at (planning AND execution)', i.e. that person is bad at planning or bad at execution (D). A, B, and C over-reach to 'everyone' or a blanket denial, which is not guaranteed.

“All bats are birds. Bats have wings. Therefore some birds have wings.” Which best evaluates this argument?

Correct: A) The form is valid, but the premise 'all bats are birds' is factually false.

The syllogistic form is valid — if the premises were true the conclusion would follow. The flaw is that the premise 'all bats are birds' is factually false; validity (form) and truth of premises are separate (A). Bats do have wings, so D is wrong.

“If someone is a full member, they hold a membership card.” A person is checked and holds a membership card. From this fact alone, what must be true?

Correct: C) This fact alone cannot decide whether they are a full member.

From 'full member → holds card', the mere possession of a card cannot establish full membership (a non-member could also be given one — affirming the consequent is invalid). So it cannot be decided (C). A commits that fallacy, and D mangles the contrapositive (the correct one is 'no card → not a full member').

About four companies' sales rankings we know: 'Alpha ranks above Beta', 'Beta ranks above Gamma', 'Delta is not ranked below Alpha'. No ties. Which company must be in 1st place?

Correct: D) Delta

Alpha > Beta > Gamma (above = better rank). 'Delta not below Alpha' with no ties means Delta > Alpha. So Delta > Alpha > Beta > Gamma, and 1st must be Delta (D). Alpha is below Delta, so A is wrong, and the order is fully forced, so C is wrong.

What is the correct negation of “there exists a meeting that every employee attended”? (mind the scope)

Correct: C) For every meeting, at least one employee did not attend it.

The claim is existential: 'some meeting exists that all employees attended' (∃meeting ∀employee attended). Its negation is 'no such meeting exists' — for every meeting, at least one employee did not attend it (C). A only fixes a single meeting and negates the 'every employee' part, leaving the 'exists' claim un-negated, so it is wrong. B is a stronger, unrelated claim, and D is irrelevant.

All roses are flowers. All flowers are plants. Which conclusion must be true?

Correct: C) All roses are plants.

Transitive inclusion: rose ⊆ flower ⊆ plant, so every rose is a plant (C). A reverses the relation, B contradicts the premise, and D over-restricts — none is guaranteed.

“If you flip the switch, the fan spins.” You flipped the switch. What must be true?

Correct: B) The fan spins.

This is affirming the antecedent (modus ponens): the antecedent 'flipped' holds, so the consequent 'spins' must follow (B). C affirms the consequent, an invalid direction that is not guaranteed.

A river is longer than a pool. A pool is longer than a pond. Which must be true?

Correct: A) The river is longer than the pond.

'Longer than' is transitive: river > pool > pond, so river > pond (A). C reverses it, B is wrong since the river is longest, and D has no basis in the premises.

What is the logical negation of “All the books on this shelf are new”?

Correct: D) At least one book is not new.

The negation of 'all are new' is 'at least one is not new' (D). A and B state the contrary (none is new), not the negation, and C is consistent with the original claim, so it does not negate it.

All surgeons are careful. Some lecturers are surgeons. Which must be true?

Correct: B) Some lecturers are careful.

Some lecturers are surgeons, and surgeons are careful, so some lecturers are careful (B). A over-strengthens to 'all', C reverses the relation, and D contradicts the premises — all exceed what is guaranteed.

“If you pour water, the seed sprouts.” The seed did not sprout. What must be true?

Correct: A) Water was not poured.

Contrapositive: 'did not sprout' implies 'water not poured'. Had water been poured, it would have sprouted; since it did not, water was not poured (A). C guesses at a cause not in the premises, so it is not guaranteed.

Lin is faster than Mei. Noah is faster than Lin. Mei is faster than Kei. Who is the fastest?

Correct: D) Noah

Noah > Lin > Mei and Mei > Kei, so overall Noah > Lin > Mei > Kei. The fastest is Noah (D). Kei is the slowest, so C is wrong.

What is the logical negation of “Some products are on sale”?

Correct: A) No product is on sale.

'Some are (at least one exists)' is negated by 'none are (all are not)' (A). B merely says some others are not, which is compatible with the original, and D is the same; C moves in the wrong direction.

All conductors carry current. Wood does not carry current. Which must be true?

Correct: C) Wood is not a conductor.

This uses the contrapositive: 'conductor → carries current' gives 'does not carry current → not a conductor'. Wood does not carry current, so wood is not a conductor (C). B is the converse and fails because non-conductors can also carry current.

“If you pass the interview, you get an offer. If you get an offer, you can join.” Rei passed the interview. What must be true?

Correct: D) Rei can join.

Chain the conditionals: pass → offer → can join, so Rei can join (D). A and B guess at choices not in the premises and are not guaranteed.

Five books sit left to right on a shelf. Blue is immediately to the right of Red. Green is somewhere to the left of Red. Yellow is immediately to the right of Blue. Which ordering statement must be true? (left to right)

Correct: B) Green is always to the left of Blue.

The fixed block is Green … Red, Blue, Yellow (Blue right of Red, Yellow right of Blue, Green left of Red), so Green is left of Blue (B). Another book could sit right of Yellow, so A is unsettled; one could sit left of Green, so C is unsettled; a book could sit between Red and Green, so D is unsettled too.

It turns out that “everyone on this team is good at both planning and execution” is false. Which must be true?

Correct: D) At least one person is bad at planning or bad at execution (at least one of the two).

Negating 'everyone is good at (planning AND execution)' gives 'at least one person is not good at (planning AND execution)', i.e. that person is bad at planning or bad at execution (D). A, B, and C over-reach to 'everyone' or a blanket denial, which is not guaranteed.

“All bats are birds. Bats have wings. Therefore some birds have wings.” Which best evaluates this argument?

Correct: A) The form is valid, but the premise 'all bats are birds' is factually false.

The syllogistic form is valid — if the premises were true the conclusion would follow. The flaw is that the premise 'all bats are birds' is factually false; validity (form) and truth of premises are separate (A). Bats do have wings, so D is wrong.

“If someone is a full member, they hold a membership card.” A person is checked and holds a membership card. From this fact alone, what must be true?

Correct: C) This fact alone cannot decide whether they are a full member.

From 'full member → holds card', the mere possession of a card cannot establish full membership (a non-member could also be given one — affirming the consequent is invalid). So it cannot be decided (C). A commits that fallacy, and D mangles the contrapositive (the correct one is 'no card → not a full member').

About four companies' sales rankings we know: 'Alpha ranks above Beta', 'Beta ranks above Gamma', 'Delta is not ranked below Alpha'. No ties. Which company must be in 1st place?

Correct: D) Delta

Alpha > Beta > Gamma (above = better rank). 'Delta not below Alpha' with no ties means Delta > Alpha. So Delta > Alpha > Beta > Gamma, and 1st must be Delta (D). Alpha is below Delta, so A is wrong, and the order is fully forced, so C is wrong.

What is the correct negation of “there exists a meeting that every employee attended”? (mind the scope)

Correct: C) For every meeting, at least one employee did not attend it.

The claim is existential: 'some meeting exists that all employees attended' (∃meeting ∀employee attended). Its negation is 'no such meeting exists' — for every meeting, at least one employee did not attend it (C). A only fixes a single meeting and negates the 'every employee' part, leaving the 'exists' claim un-negated, so it is wrong. B is a stronger, unrelated claim, and D is irrelevant.

All roses are flowers. All flowers are plants. Which conclusion must be true?

Correct: C) All roses are plants.

Transitive inclusion: rose ⊆ flower ⊆ plant, so every rose is a plant (C). A reverses the relation, B contradicts the premise, and D over-restricts — none is guaranteed.

“If you flip the switch, the fan spins.” You flipped the switch. What must be true?

Correct: B) The fan spins.

This is affirming the antecedent (modus ponens): the antecedent 'flipped' holds, so the consequent 'spins' must follow (B). C affirms the consequent, an invalid direction that is not guaranteed.

A river is longer than a pool. A pool is longer than a pond. Which must be true?

Correct: A) The river is longer than the pond.

'Longer than' is transitive: river > pool > pond, so river > pond (A). C reverses it, B is wrong since the river is longest, and D has no basis in the premises.

What is the logical negation of “All the books on this shelf are new”?

Correct: D) At least one book is not new.

The negation of 'all are new' is 'at least one is not new' (D). A and B state the contrary (none is new), not the negation, and C is consistent with the original claim, so it does not negate it.

All surgeons are careful. Some lecturers are surgeons. Which must be true?

Correct: B) Some lecturers are careful.

Some lecturers are surgeons, and surgeons are careful, so some lecturers are careful (B). A over-strengthens to 'all', C reverses the relation, and D contradicts the premises — all exceed what is guaranteed.

“If you pour water, the seed sprouts.” The seed did not sprout. What must be true?

Correct: A) Water was not poured.

Contrapositive: 'did not sprout' implies 'water not poured'. Had water been poured, it would have sprouted; since it did not, water was not poured (A). C guesses at a cause not in the premises, so it is not guaranteed.

Lin is faster than Mei. Noah is faster than Lin. Mei is faster than Kei. Who is the fastest?

Correct: D) Noah

Noah > Lin > Mei and Mei > Kei, so overall Noah > Lin > Mei > Kei. The fastest is Noah (D). Kei is the slowest, so C is wrong.

What is the logical negation of “Some products are on sale”?

Correct: A) No product is on sale.

'Some are (at least one exists)' is negated by 'none are (all are not)' (A). B merely says some others are not, which is compatible with the original, and D is the same; C moves in the wrong direction.

All conductors carry current. Wood does not carry current. Which must be true?

Correct: C) Wood is not a conductor.

This uses the contrapositive: 'conductor → carries current' gives 'does not carry current → not a conductor'. Wood does not carry current, so wood is not a conductor (C). B is the converse and fails because non-conductors can also carry current.

“If you pass the interview, you get an offer. If you get an offer, you can join.” Rei passed the interview. What must be true?

Correct: D) Rei can join.

Chain the conditionals: pass → offer → can join, so Rei can join (D). A and B guess at choices not in the premises and are not guaranteed.

Five books sit left to right on a shelf. Blue is immediately to the right of Red. Green is somewhere to the left of Red. Yellow is immediately to the right of Blue. Which ordering statement must be true? (left to right)

Correct: B) Green is always to the left of Blue.

The fixed block is Green … Red, Blue, Yellow (Blue right of Red, Yellow right of Blue, Green left of Red), so Green is left of Blue (B). Another book could sit right of Yellow, so A is unsettled; one could sit left of Green, so C is unsettled; a book could sit between Red and Green, so D is unsettled too.

It turns out that “everyone on this team is good at both planning and execution” is false. Which must be true?

Correct: D) At least one person is bad at planning or bad at execution (at least one of the two).

Negating 'everyone is good at (planning AND execution)' gives 'at least one person is not good at (planning AND execution)', i.e. that person is bad at planning or bad at execution (D). A, B, and C over-reach to 'everyone' or a blanket denial, which is not guaranteed.

“All bats are birds. Bats have wings. Therefore some birds have wings.” Which best evaluates this argument?

Correct: A) The form is valid, but the premise 'all bats are birds' is factually false.

The syllogistic form is valid — if the premises were true the conclusion would follow. The flaw is that the premise 'all bats are birds' is factually false; validity (form) and truth of premises are separate (A). Bats do have wings, so D is wrong.

“If someone is a full member, they hold a membership card.” A person is checked and holds a membership card. From this fact alone, what must be true?

Correct: C) This fact alone cannot decide whether they are a full member.

From 'full member → holds card', the mere possession of a card cannot establish full membership (a non-member could also be given one — affirming the consequent is invalid). So it cannot be decided (C). A commits that fallacy, and D mangles the contrapositive (the correct one is 'no card → not a full member').

About four companies' sales rankings we know: 'Alpha ranks above Beta', 'Beta ranks above Gamma', 'Delta is not ranked below Alpha'. No ties. Which company must be in 1st place?

Correct: D) Delta

Alpha > Beta > Gamma (above = better rank). 'Delta not below Alpha' with no ties means Delta > Alpha. So Delta > Alpha > Beta > Gamma, and 1st must be Delta (D). Alpha is below Delta, so A is wrong, and the order is fully forced, so C is wrong.

What is the correct negation of “there exists a meeting that every employee attended”? (mind the scope)

Correct: C) For every meeting, at least one employee did not attend it.

The claim is existential: 'some meeting exists that all employees attended' (∃meeting ∀employee attended). Its negation is 'no such meeting exists' — for every meeting, at least one employee did not attend it (C). A only fixes a single meeting and negates the 'every employee' part, leaving the 'exists' claim un-negated, so it is wrong. B is a stronger, unrelated claim, and D is irrelevant.