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Unit 1 · Discrete Structures and Optimisation Paper 2 CS · 22 June 2026

Match the LIST-I with LIST-II. Match the equivalent propositions in List-I and List-II
LIST-ILIST-II
A. P→(Q→P)I. (P∨Q)∧¬(P∧Q)
B. P→(Q∨R)II. (P∨R)→Q
C. (P→Q)∧(R→Q)III. (P→Q)∨(P→R)
D. ¬(P⇔Q)IV. ¬P→(P→Q)
Choose the correct answer from the options given below:

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Correct answer: B. A-IV, B-III, C-II, D-I

Explanation

A: P→(Q→P) ≡ ¬P∨¬Q∨P ≡ True, and IV: ¬P→(P→Q) ≡ P∨¬P∨Q ≡ True, so both are tautologies and A≡IV. B: P→(Q∨R) ≡ ¬P∨Q∨R, and III: (P→Q)∨(P→R) ≡ (¬P∨Q)∨(¬P∨R) ≡ ¬P∨Q∨R, so B≡III. C: (P→Q)∧(R→Q) ≡ (¬P∨Q)∧(¬R∨Q) ≡ Q∨(¬P∧¬R) ≡ Q∨¬(P∨R) ≡ (P∨R)→Q, matching II. D: ¬(P⇔Q) is exclusive-or, which equals (P∨Q)∧¬(P∧Q), matching I. So the matching is A-IV, B-III, C-II, D-I.

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