Embibe Experts Solutions for Exercise 1: Assignment

Write the negation of following sentences in three ways and also write interpretation of negation of statement
$q:$ Every quadratic equation has two real roots.

Write the rules regarding the connective "OR" to prove a compound statement with example.

Rewrite the following statement with "If then" in five different ways conveying the same meaning.
$p:$If two circles are apart from each other, then we can draw four common tangents to them.

Check whether "OR" used in the following compound statement is exclusive or inclusive? Write the component statements of the compound statements and use them to check whether compound statement is true or not. Justify your answer.

$p:$ A quadratic equation has real or complex root.

Verify by method of contradiction
$p:$ For every real number $x\in \left[0,\frac{\pi }{2}\right]$, we have $\sin x+\cos x\ge 1$.

Verify by the method of contradiction
$p:$ The product of a non-zero rational number and an irrational number is an irrational number.

By giving a counter example show that $p$ is false

$p:$For all integers $a,b$and $c$ if $a\mid bc$ then $a\mid b$ or $a\mid c$.

For the given statement identify the necessary and sufficient condition.

$r:$ If you pass $\mathrm{NTSE}$ Test then you will get scholarship.