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Match the LIST-I with LIST-II: Match the logical equivalence propositions

LIST - I

LIST - II

A.

P → q

I.

(p ∧ q) ∨(¬p ∨ ¬q)

B.

¬(p ∨ (¬p ∧ q))

II.

¬p ∨ q

C.

p ↔ q

III.

¬(p ∨ q)

D.

¬(p ↔ q)

IV.

¬p ↔ q


Choose the correct answer from the options given below:

  1. A - I, B - III, C - II, D - IV 
  2. A - I, B - II, C - III, D - IV 
  3. A - II, B - III, C - I, D - IV 
  4. A - II, B - III, C - IV, D - I

Answer (Detailed Solution Below)

Option 3 : A - II, B - III, C - I, D - IV 

Detailed Solution

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The correct answer is Option 3.

key-point-imageKey Points

Let's match the logical equivalence propositions between LIST-I and LIST-II:

LIST - I LIST - II
A. P → q II. ¬p ∨ q
B. ¬(p ∨ (¬p ∧ q)) III. ¬(p ∨ q)
C. p ↔ q I. (p ∧ q) ∨ (¬p ∨ ¬q)
D. ¬(p ↔ q) IV. ¬p ↔ q

The matchings are:

  • A - II: P → q is logically equivalent to ¬p ∨ q
  • B - III: ¬(p ∨ (¬p ∧ q)) is logically equivalent to ¬(p ∨ q)
  • C - I: p ↔ q is logically equivalent to (p ∧ q) ∨ (¬p ∨ ¬q)
  • D - IV: ¬(p ↔ q) is logically equivalent to ¬p ↔ q

Therefore, the correct option is Option 3.

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