Amit M Agarwal Solutions for Chapter: Mathematical Reasoning, Exercise 1: Work Book Exercise

Negation of $2+3=5$ and $8<10$ is

If Ram secures $100$ marks in Mathematics, then he will get a mobile. The converse is

For the following three statements
$p: 2$ is an even number.
$q: 2$ is a prime number.
$r :$ Sum of two prime numbers is always even.
Then, the symbolic statements $\left(p\wedge q\right)\to ~r$ means

The dual of the statement $\left(p\wedge q\right)\wedge ~q\equiv \left(p\vee ~q\right)$ is

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

Which of the following is always true?

Let $p$ and $q$ be two statements. Then, $\left(~p\vee q\right)\wedge \left(~p\wedge ~q\right)$ is a

Which of the following is wrong statement?