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Construct the truth table of the following statement pattern. ∼ p ∧ [(p ∨ ∼ q) ∧ q] - Mathematics and Statistics

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Question

Construct the truth table of the following statement pattern.

∼ p ∧ [(p ∨ ∼ q) ∧ q]

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Solution

p q ∼ p ∼ q p ∨ ∼ q (p ∨ ∼ q) ∧ q ∼ p ∧ [(p ∨ ∼ q) ∧ q]
T T F F T T F
T F F T T F F
F T T F F F F
F F T T T F F
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Chapter 1: Mathematical Logic - Exercise 1.2 [Page 13]

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Using truth table prove that:

~ (p `leftrightarrow` q) ≡ (p ∧ ~ q) ∨ (q ∧ ~ p)


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