Maharashtra Board Solutions for Chapter: Mathematical Logic, Exercise 1: Exercise 1.1

If the statements $p,q$ are true statements and $r,s$ are false statements then determine the truth values of the following.

$\left(~r\leftrightarrow p\right)\to ~q$

If the statements $p,q$ are true statements and $r,s$ are false statements then determine the truth values of the following.

$\left[~p\wedge \left(~q\wedge r\right)\right]\vee \left[\left(q\wedge r\right)\vee \left(p\wedge r\right)\right]$

If the statements $p,q$ are true statements and $r,s$ are false statements then determine the truth values of the following.

$\left[\left(~p\wedge q\right)\wedge ~r\right]\vee \left[\left(q\to p\right)\to \left(~s\vee r\right)\right]$

If the statements $p,q$ are true statements and $r,s$ are false statements then determine the truth values of the following.

$~\left[\left(~p\wedge r\right)\vee \left(s\to ~q\right)\right]\leftrightarrow \left(p\wedge r\right)$

Write the negation of the following.

$3$ is not a root of the equation $x^2+3x-18=0$

Write the negation of the following.

$\sqrt{2}$ is a rational number.

Write the negation of the following.

Polygon $ABCDE$ is a pentagon.

Write the negation of the following.

$7+3>5$