Question

If $p$ is any statement, $t$ is a tautology and $c$ is a contradiction, then which for the following is NOT correct?

• A. $p\wedge (\sim c)\equiv p$
• B. $p\vee (\sim t)\equiv p$
• C. $t\vee c\equiv p\vee t$
• D. $(p\wedge t)\vee (p\vee c)\equiv (t\wedge c)$

Answer 1

Answer: (D)

$(p\wedge t)\vee (p\vee c)\equiv (t\wedge c)$

A. $p\wedge (\sim c)\equiv p\wedge t\equiv p$

B. $p\vee (\sim t)\equiv p\vee c\equiv p$

C. $t\vee c\equiv t\equiv p\vee t$

Clearly option 'A', 'B', 'C' are correct.

Hence option 'D' is the correct choice.