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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?

  1. (p ∧ q) ∧ ¬(p ∨ q)
  2. p ∨ (¬p ∧ q)
  3. (p ⇒ q) ⇒ p
  4. None of these
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Solution

The first statement is a contradiction.

Here's why:

  1. The statement (p∧q)∧~(p∨q) can be broken down into two parts: (p∧q) and ~(p∨q).

  2. The first part (p∧q) means that both p and q are true.

  3. The second part ~(p∨q) is the negation of (p∨q), which means that both p and q are not true.

  4. Therefore, the whole statement is saying that p and q are both true and not true at the same time, which is a contradiction.

This problem has been solved

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