Match the LIST-I with LIST-II: Match the logical equivalence propositions
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LIST - I
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LIST - II
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A.
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P → q
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I.
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(p ∧ q) ∨(¬p ∨ ¬q)
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B.
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¬(p ∨ (¬p ∧ q))
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II.
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¬p ∨ q
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C.
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p ↔ q
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III.
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¬(p ∨ q)
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D.
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¬(p ↔ q)
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IV.
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¬p ↔ q
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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 ✓ Correct
4.A - II, B - III, C - IV, D - I
Solution
The correct answer is Option 3.
Key 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.