Question

If $A=\{1,2,3,4\}.$, then number of statements from the below having truth value as true is
$\left(1\right)\exists x\in A$ such that $x+3=8$
$\left(2\right)\forall x\in A,x+2<7.$
$\left(3\right)\forall x\in A$ such that $x+1<3.$
$\left(4\right)\forall x\in A,x+3\ge 5.$

Answer 1

$\left(1\right)$ Clearly, no number in $A$ satisfies $x+3=8.$
$\therefore$ the given statement is false.

$\left(2\right)$ Every number in $A$ satisfies $x+2<7.$
So, given statement is true.

$\left(3\right)$ Clearly, $x=4\in A$ doesnot satisfies $x+1<3.$
$\therefore$ the given statement is false.

$\left(4\right)$ Since $x=1\in A$ does not satisfy $x+3\ge 5,$ the statement is false.
Clearly we can say that we have 2 true statements.