Question

Write negation of the following statements

a)The number 6 is an even number or the number 25 is a perfect square.

b) $Ifx\in A\cap B,thenx\in Andx\in b$

Answer 1

$a)P:6$ is an even number.

$q:25$ is a perfect square.

Symbolic form$:\sim (p\vee q)\equiv \sim p\wedge \sim q$

Negation$:6$ is not an even number and $25$ is not a perfect square.

$b)$If $x\in A\cap B\Rightarrow x\in A$ and $x\in B$

Its Negation is $x\notin A$ and $x\notin B$

$\Rightarrow x\notin A\cap B$

$\Rightarrow x\in A\cup B$