Embibe Experts Solutions for Chapter: Mathematical Reasoning, Exercise 1: Exercise 1

Consider the statement $p$ : "New Delhi is a city". Which of the following is not negation of $p$?

If $p, q$ and $r$ are statements with truth values false, true and false respectively, then the truth value of $\left(~p\vee ~q\right)\vee r$ is

The statement $~(p\wedge q)\vee q$

If $p, q, r$ are simple propositions, then the truth value of $(~p\vee q)\wedge ~r\Rightarrow p$ is

Which of the following is a tautology?

Which of the following is always true?

The statement $p\wedge \left(~q\vee r\right)\wedge \left(~r\vee q\right)$ is

Statement I :  $~\left(A\iff ~B\right)$ is equivalent to $A\iff B.$
Statement II :  $A\vee \left(~\left(A\wedge ~B\right)\right)$ a tautology.