Q.1 (i) 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 \(x + 2 \lt 9\)
C. \(\forall\, x \in A,\ x + 6 \ge 9\)
D. \(\forall\, x \in A,\ x + 5 \le 10\)
Best answer
Answer: C. \(\forall\, x \in A,\ x + 6 \ge 9\)
Answer: (c) \(\forall\, x \in A,\ x + 6 \ge 9\)
(a) is true for \(x = 5\). (b) is true, e.g. \(x = 1\) gives \(3 \lt 9\). (d) is true since the largest value is \(5 + 5 = 10\). But (c) fails for \(x = 1\): \(1 + 6 = 7\), which is not \(\ge 9\). So (c) is the statement that is not true.
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