Match List-I with List-II
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List I
Propositions
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List II
Disjunctive Normal Form (DNF)
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A.
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P ∧ (P → Q) |
I.
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P ∨ Q |
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B.
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¬ (P ∨ Q) → (P ∧ Q) |
II.
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(P ∧ ¬ P) ∨ (P ∧ Q) |
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C.
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P → Q |
III.
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(¬ P) ∨ Q |
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D.
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P ∨ (Q ∧ R) |
IV.
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(P ∧ P) ∨ (P ∧ Q) ∨ (P ∧ R) ∨ (Q ∧ R) |
Choose the correct answer from the options given below :
1.A - I, B - II, C - III, D - IV
2.A - II, B - I, C - III, D - IV ✓ Correct
3.A - III, B - I, C - II, D - IV
4.A - IV, B - III, C - II, D - I
Solution
The correct answer is A - II, B - I, C - III, D - IV
EXPLANATION:
Option A: P ∧ (P → Q)
- P ∨ ¬ P ∨ Q
- P ∧ ¬ P ∨ P ∨ Q
- This Propositions match from Disjunctive Normal Form list option II
Option B: ¬ (P ∨ Q) → (P ∧ Q)
- ¬ ¬ (P ∨ Q) v (P ∧ Q)
- (P ∨ Q) v (P ∧ Q)
- (P ∨ Q)
- This Propositions match from Disjunctive Normal Form list option I
Option C: P → Q
- P → Q
- ¬ P ∨ Q
- This Propositions match from Disjunctive Normal Form list option III
Option D: P ∨ (Q ∧ R)
- P ∨ (Q ∧ R)
- (P ∧ P) ∨ (P ∧ Q) ∨ (P ∧ R) ∨ (Q ∧ R)
- This Propositions match from Disjunctive Normal Form list option IV