Question

If A = {3, 4, 6, 8}, determine the truth value of each of the following: 

i. \(\exists\) x \(\in\) A, such that x + 4 = 7 

ii. \(\forall\) x \(\in\) A, x + 4 < 10.

iii. \(\forall\) x \(\in\) A, x + 5 \(\geq\) 13. 

iv. \(\exists\) x \(\in\) A, such that x is odd. 

v. \(\exists\) x \(\in\) A, such that (x -3) \(\in\) N

Answer 1

i. Since x = 3 \(\in\) A, satisfies x + 4 = 7 

\(\therefore\) the given statement is true. 

\(\therefore\) Its truth value is ‘T’.

ii. Since x = 6, 8 \(\in\) A, do not satisfy x + 4 < 10, 

\(\therefore\) the given statement is false. 

\(\therefore\) Its truth value is ‘F’

iii. Since x = 3, 4, 6 \(\in\) A, do not satisfy x + 5 \(\geq\) 13, 

\(\therefore\) the given statement is false. 

\(\therefore\) Its truth value is ‘F’.

iv. Since x = 3 \(\in\) A, satisfies the given statement, 

\(\therefore\) the given statement is true. 

\(\therefore\)Its truth value is ‘T’.

v. Since x = 4, 6, 8 \(\in\) A, satisfy (x - 3) \(\in\) N,

\(\therefore\) the given statement is true.

\(\therefore\) Its truth value is ‘T’.