Maharashtra State BoardHSC Arts 12th Board Exam
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Using the truth table prove the following logical equivalence. p → (q → p) ≡ ∼ p → (p → q) - Mathematics and Statistics

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Using the truth table prove the following logical equivalence.

p → (q → p) ≡ ∼ p → (p → q)

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Solution

1 2 3 4 5 6 7
p q q → p p → (q → p) ∼ p p → q ∼ p → (p → q)
T T T T F T T
T F T T F F T
F T F T T T T
F F T T T T T

The entries in columns 4 and 7 are identical.
∴ p → (q → p) ≡ ∼ p → (p → q)

Concept: Statement Patterns and Logical Equivalence
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