Logic Questions and Answers

Answer: D

Correct answer: 3, 5, 1, 4, 2

The sequence follows the natural order of cause and effect. Study comes first, then the exam that tests it, then the job the qualification obtains, then the income the job brings, and finally the independence the income makes possible. Each step is the precondition of the one after it.

Answer: D

Correct answer: Sonam

David is below Dechen and above Sonam, and Karma is above David. So Dechen and Karma are both above David and Sonam is the only one below him. The ordering is not complete - nothing settles whether Dechen or Karma is higher - but the bottom position is determined, and it is Sonam’s.

Answer: C

Correct answer: If p is true and q is false and r is false, the P1 is true

Conjunction binds more tightly than disjunction, so the formula reads \( [(p \lor \lnot q) \land (q \to r)] \lor (r \lor p) \). With p true, q false and r false: \( p \lor \lnot q \) is true, \( q \to r \) is true because the antecedent is false, so the bracket is true and the whole is true. It is not a tautology, since p false, q true and r false makes every disjunct false.

Answer: A

Correct answer: ((P → Q)^(Q → R))→ (P → R)

This is the hypothetical syllogism and it is valid: if P leads to Q and Q leads to R, then P leads to R. The second option is the fallacy of denying the antecedent, the third fails when P is false and Q false, and the fourth confuses the disjunction of two implications with the implication of a disjunction.

Answer: C

Correct answer: aunt

Take the description from the inside out. The husband of Robin’s mother is Robin’s father; the mother of Robin’s father is Robin’s grandmother; and the daughter of that grandmother is Robin’s father’s sister. A father’s sister is an aunt.

Answer: B

Correct answer: a ^ b → b v c

If the antecedent \( a \land b \) is true then b is true, so \( b \lor c \) is true and the implication holds; if the antecedent is false the implication holds vacuously. The other two fail: the first when a is true and b false, and the third when a is false, b true and c false.

Answer: D

Correct answer: Soles

The question asks what a shoe must have by definition rather than what it commonly has. Laces, leather and straps all appear on some shoes and not others - a slip-on has no laces, a canvas shoe no leather. A sole is what makes the object a shoe at all, so it is the only universal.

Answer: A

Correct answer: History

Chain the preferences together. Social science is preferred to Maths and Maths to History, and English is preferred to Social science, giving English above Social science above Maths above History. Economics is above Maths and Political Science above History. Nothing is placed below History, so it is the least preferred.

Answer: B

Correct answer: Wednesday

Count forward from the fixed point. The day before yesterday was Saturday, so yesterday was Sunday and today is Monday. Tomorrow is Tuesday and the day after tomorrow is Wednesday. The whole difficulty of such questions is keeping the anchor straight, so it is worth naming today explicitly before counting on.

Answer: C

Correct answer: F1 is satisfiable, F2 is valid

F1 is \( P \to \lnot P \), which reduces to \( \lnot P \); that is true when P is false, so F1 is satisfiable though not valid. F2 is \( (P \to \lnot P) \lor (\lnot P \to P) \), which reduces to \( \lnot P \lor P \) and is therefore true in every case, so F2 is valid.