Statements, Syllogism & Deduction› Logical Deduction & Truth Puzzles
P, Q, R and S are four statements. Relation between these statements is as follows : I. If P is true, then Q must be true. II. If Q is true, then R must be true. III. If S is true, then either Q is false or R is false. Which of the following must be true ?
Answer a.
Option a: if P is true then Q and R are both true, and statement III then forbids S, so S must be false. Suppose P is true. By I, Q is true; by II, R is then true. Statement III says that if S is true, at least one of Q and R is false. With Q and R both true, S cannot be true (contrapositive of III), so S is false. Hence 'If P is true, then S is false' must hold. The other options reverse an implication or claim something the conditions do not force, and each can be refuted by an assignment that satisfies I, II and III.
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