Match List-I with List-II and choose the correct answer from the code…
2018
Match List-I with List-II and choose the correct answer from the code given below :
\(\begin{array}{cccc} & \textbf{List I} & & \textbf{List II} \\ (a) & Equivalence & (i) & p \Rightarrow q \\ (b) & Contrapositive & (ii) & p \Rightarrow q; q \Rightarrow p \\ (c ) & Converse & (iii) & p \Rightarrow q: \sim q \Rightarrow \sim p \\ (d) & Implication & (iv) & p \Leftrightarrow q \\ \end{array}\)
- A.
\((a)-(i), (b)-(ii), (c)-(iii), (d)-(iv) \) - B.
\((a)-(ii), (b)-(i), (c)-(iii), (d)-(iv) \) - C.
\((a)-(iii), (b)-(iv), (c)-(ii), (d)-(i) \) - D.
\((a)-(iv), (b)-(iii), (c)-(ii), (d)-(i)\)
Attempted by 251 students.
Show answer & explanation
Correct answer: D
Explanation of correct matching:
Equivalence: This is the biconditional relation p ⇔ q, so match with the expression p ⇔ q.
Contrapositive: For an implication p ⇒ q the contrapositive is ¬q ⇒ ¬p. The contrapositive is presented together with the original implication as p ⇒ q : ¬q ⇒ ¬p.
Converse: The converse of p ⇒ q is q ⇒ p. The List-II item that contains q ⇒ p is the expression p ⇒ q; q ⇒ p (which lists both directions).
Implication: This is the single-direction statement p ⇒ q, so match with p ⇒ q.
Therefore the correct correspondences are: Equivalence → p ⇔ q; Contrapositive → p ⇒ q : ¬q ⇒ ¬p; Converse → p ⇒ q; q ⇒ p (converse is q ⇒ p, present in this expression); Implication → p ⇒ q.