Q.If $A = \{1, 2, 3, 4, 5\}$ then which of the following is not true?
A) $\exists\, x \in A$ such that $x + 3 = 8$
B) $\exists\, x \in A$ such that $x + 2 < 9$
C) $\forall\, x \in A,\ x + 6 \geq 9$
D) $\exists\, x \in A$ such that $x + 6 < 10$

$A = \{1,2,3,4,5\}$.

A) $\exists x\in A$ with $x+3=8$: $x=5$ works ($5+3=8$). True — not the answer.

B) $\exists x\in A$ with $x+2<9$: $x=1$ works ($1+2=3<9$). True — not the answer.

C) $\forall x\in A,\ x+6\geq 9$, i.e. $x\geq 3$ for every $x$: but $x=1$ gives $1+6=7 < 9$, and $x=2$ gives $2+6=8<9$ — the claim fails for these. So this universal statement is False — this is the one that is NOT …

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