D.P. GUPTA, Preetima Bajpai and, Sanjeev Kumar Jha Solutions for Chapter: Mathematical Reasoning, Binary Operation and Group Theory, Exercise 1: Exercise 1

Let $G$ denote the set of all $n\times n$ non-singular matrices with rational numbers as entries. Then under multiplication

If truth values of $p$ be $F$ and $q$ be $T.$ Then, the truth value of $~\left(~p\vee q\right)$ is

Which of the following is always true?

The false statement in the following is

The statement $(p\Rightarrow q)\iff (~p\wedge q)$ is a

The negation of the compound proposition $p\vee \left(~p\vee q\right)$

The negation of the statement $(p\wedge q)\to (~p\vee r)$ is

If $N$ is a set of natural numbers, then under binary operation $a·b=a+b,( N,·)$ is