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If A = {4, 5, 7, 9}, determine the truth value of each of the following quantified statements.i. \(\exists\) x \(\in\) A, such that x + 2 = 7.ii. \(\forall\) x \(\in\) A, x + 3 < 10.iii. \(\forall\) x \(\in\) A, such that x + 5 \(\geq\)9.iv. \(\exists\) x \(\in\) A, such that x is even.v. \(\forall\) x \(\in\) A, 2x \(\leq\) 17. |
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Answer» i. Since x = 5 \(\in\) A, satisfies x + 2 = 7. \(\therefore\)the given statement is true. \(\therefore\) Its truth value is ‘T’. ii. Since, x = 7, 9 \(\in\) A, do not satisfy x + 3 < 10. \(\therefore\) the given statement is false. \(\therefore\) Its truth value is ‘F’. iii. Since, x = 4, 5, 7, 9 \(\in\) A, satisfy x + 5 \(\geq\) 9. \(\therefore\) the given statement is true. \(\therefore\) Its truth value is ‘T’. iv. Since, x = 4 \(\in\) A, satisfies ‘x is even’. \(\therefore\) the given statement is true. \(\therefore\) Its truth value is ‘T’. v. Since x = 9 \(\in\) A does not satisfy 2x \(\leq\) 17. \(\therefore\) the given statement is false. \(\therefore\) Its truth value is ‘F’. |
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