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Question
For any two statements p and q, the statement ∼(p∨q)∨(∼p∧q) is equivalent to
For any two statements p and q, the statement ∼(p∨q)∨(∼p∧q) is equivalent to
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Solution
The correct option is C ∼p
The statement ∼(p∨q)∨(∼p∧q) is equivalent to
=(∼p∧∼q)∨(∼p∧q)
=∼p∧(∼q∨q)
=∼p∧T=∼p
The statement ∼(p∨q)∨(∼p∧q) is equivalent to
=(∼p∧∼q)∨(∼p∧q)
=∼p∧(∼q∨q)
=∼p∧T=∼p
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