Which of the following is a contradiction?(p∧q)∧~(p∨q)p∨(~p∧q)(p⇒q)⇒pNone of these
Question
Which of the following is a contradiction?
- (p ∧ q) ∧ ¬(p ∨ q)
- p ∨ (¬p ∧ q)
- (p ⇒ q) ⇒ p
- None of these
Solution
The first statement is a contradiction.
Here's why:
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The statement (p∧q)∧~(p∨q) can be broken down into two parts: (p∧q) and ~(p∨q).
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The first part (p∧q) means that both p and q are true.
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The second part ~(p∨q) is the negation of (p∨q), which means that both p and q are not true.
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Therefore, the whole statement is saying that p and q are both true and not true at the same time, which is a contradiction.
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