Using truth table prove that ~ p ˄ q ≡ ( p ˅ q) ˄ ~ p - Mathematics and Statistics

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Using truth table prove that ~ p ˄ q ≡ ( p ˅ q) ˄ ~ p

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Solution

~ p ∧ q ≡ (p ∨ q) ∧ ~ p

1 2 3 4 5 6
p q ~p ~p ∧ q (p ∨ q) (p ∨ q) ∧ ~p
T T F F T F
T F F F T F
F T T T T T
F F T F F F

In the above truth table, the entries in the columns 4 and 6 are identical.

∴ ~p ∧ q ≡ (p ∨ q) ∧ ~p.

  Is there an error in this question or solution?
Chapter 1.1: Mathematical Logic - Q.4

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