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Question
The expression (p ∧∼q)∨q∨(∼p∧q) is equivalent to
The expression (p ∧∼q)∨q∨(∼p∧q) is equivalent to
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Solution
The correct option is B p∨q
[(p ∧∼q)∨q]∨(∼p∧q)
=[(p∨q)∧(∼q∨q)]∨(∼p∧q)
=[(p∨q)∧T]∨(∼p∧q)
=(p∨q)∧[T∨(∼p∧q)]=(p∨q)∧T=p∨q
[(p ∧∼q)∨q]∨(∼p∧q)
=[(p∨q)∧(∼q∨q)]∨(∼p∧q)
=[(p∨q)∧T]∨(∼p∧q)
=(p∨q)∧[T∨(∼p∧q)]=(p∨q)∧T=p∨q
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