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Using truth table prove that p ↔ q = (p ∧ q) ∨ (~p ∧ ~q). - Mathematics and Statistics

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Using truth table prove that p ↔ q = (p ∧ q) ∨ (~p ∧ ~q).

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Solution

1 2 3 4 5 6 7 8
p q p ↔ q ~p ~q p ∧ q ~p ∧ ~q (p ∧ q) ∨(~p∧~q)
T T T F F T F T
T F F F T F F F
F T F T F F F F
F F T T T F T T

 

The entries in columns 3 and 8 are identical.

p ↔ q = (p ∧ q) ∨ (~p ∧ ~q).

Notes

[1 mark each for column 3 and column 8]

Concept: Logical Connective, Simple and Compound Statements
  Is there an error in this question or solution?

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