Question

If \(A = \{1,2,3,4,5,6\}\) then which of the following is not true?

• A. \(\exists x\in A\) such that \(x+3 = 9\).
• B. \(\exists x\in A\) such that \(x+2 < 9\).
• C. \(\forall x\in A,x+6\geq 10\).
• D. \(\exists x\in A\) such that \(x+6 < 10\).

Hint:

Test each statement against the set; a "for all" statement fails if one element breaks it.

Answer 1

The Correct Option is C

Step 1: Find the failing element:
For $\forall x\in A,\ x+6\geq10$, the elements 1, 2, 3 give 7, 8, 9, all below 10. So the statement fails.

Step 2: Confirm the others:
(A) is satisfied by 6, (B) by 1, (D) by 1.

Step 3: Pick:
Option C.

Final Answer:
x = 1 gives 7, so the "for all x" statement in C fails. \[ \boxed{\text{(C) }\forall x\in A,\ x+6\geq10} \]