R S Aggarwal Solutions for Exercise 3: EXERCISE

Write the converse and contrapositive of the statement "If it rains, then I stay at home".

Given that $p:$ If a quadrilateral is equiangular, then it is a rectangle, $q:$ If a quadrilateral is a rectangle, then it is equiangular,are some pairs of statements . Combine the pair of these statements using if and only if

Given that  $p:$ If the sum of the digits of a number is divisible by $3$, then the number is divisible by $3$,and  $q:$ If a number is divisble by $3$, then the sum of its digits is divisible by $3$,  are some pairs of statements.  Combine these pair of stayements using "if and only if"

Given below are some pairs of statements. Combine each pair using if and only if:

$p:$ A quadrilateral is a parallelogram if its diagonals bisect each other.

$q:$ If the diagonals of a quadrilateral bisect each other, then it is a parallelogram.

Given below are some pairs of statements. Combine each pair using if and only if:

$p:$ If $f\left(a\right)=0$ then $\left(x-a\right)$ is a factor of polynomial $f\left(x\right)$

$q:$ If $\left(x-a\right)$ is a factor of polynomial $f\left(x\right)$ then $f\left(a\right)=0$

Given below are some pairs of statements. Combine each pair using if and only if:

$p:$ If a square matrix $A$ is invertible, then $\left|A\right|$ is nonzero.

$q:$ If $A$ is a square matrix such that $\left|A\right|$ is nonzero, then $A$ is invertible.

Write the statement "In order to get $A$ grade, it is necessary and sufficient that you do all the homework regularly" using 'if and only if'

Write the following using 'if and only if':

If you watch television then your mind is free and if your mind is free then you watch television