Question

Prove that following Logical Equivalence with out using truth tables:

1. [P V Q V (~P ^ ~Q^ R) ≡ (P V Q V R)

Answer 1

Answer:

Solution

verified

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L.H.S. =p↔q

=(p→q)∧(q→p)

=(p∨∼q)∧(q∨∼p)

=((p∨∼q)∧q)∨((p∨∼q)∧∼p)

=((p∧q)∨(∼q∧q))∨((p∧∼p)∨(∼q∧∼p))

=(p∧q)∨(∼p∧∼q)

= R.H.S.

Hence proved.