If A = {3, 5, 7, 9, 11, 12}, determine the truth value of each of the

1.	If A = {3, 5, 7, 9, 11, 12}, determine the truth value of each of the following :(i) Ǝ x ∈ A such that x – 8 = 1(ii) \(\forall\) x ∈ A, x2 + x is an even number.(iii) Ǝ x ∈ A such that x2 < 0(iv) \(\forall\) x ∈ A, x is an even number.(v) Ǝ x ∈ A such that 3x + 8 > 40(vi) \(\forall\) x ∈ A, 2x + 9 > 14
Answer» (i) Ǝ x ∈ A such that x – 8 = 1 Clearly x = 9 ∈ A satisfies x – 8 = 1. So the given statement is true, hence its truth value is T. (ii) \(\forall\) x ∈ A, x² + x is an even number. For each x ∈ A, x² + x is an even number. So the given statement is true, hence its truth value is T. (iii) Ǝ x ∈ A such that x² < 0 There is no x ∈ A which satisfies x² < 0. So the given statement is false, hence its truth value is F. (iv) \(\forall\) x ∈ A, x is an even number. x = 3 ∈ A, x = 5 ∈ A, x = 7 ∈ A, x = 9 ∈ A, x = 11 ∈ A do not satisfy x is an even number. So the given statement is false, hence its truth value is F. (v) Ǝ x ∈ A such that 3x + 8 > 40 Clearly x = 11 ∈ A and x = 12 ∈ A satisfies 3x + 8 > 40. So the given statement is true, hence its truth value is T. (vi) \(\forall\) x ∈ A, 2x + 9 > 14 For each x ∈ A, 2x + 9 > 14. So the given statement is true, hence its truth value is T.

If A = {3, 5, 7, 9, 11, 12}, determine the truth value of each of the following :(i) Ǝ x ∈ A such that x – 8 = 1(ii) \(\forall\) x ∈ A, x2 + x is an even number.(iii) Ǝ x ∈ A such that x2 < 0(iv) \(\forall\) x ∈ A, x is an even number.(v) Ǝ x ∈ A such that 3x + 8 > 40(vi) \(\forall\) x ∈ A, 2x + 9 > 14

Answer»

(i) Ǝ x ∈ A such that x – 8 = 1

Clearly x = 9 ∈ A satisfies x – 8 = 1.

So the given statement is true, hence its truth value is T.

(ii) \(\forall\) x ∈ A, x² + x is an even number.

For each x ∈ A,

x² + x is an even number.

So the given statement is true, hence its truth value is T.

(iii) Ǝ x ∈ A such that x² < 0

There is no x ∈ A which satisfies x² < 0.

So the given statement is false, hence its truth value is F.

(iv) \(\forall\) x ∈ A, x is an even number.

x = 3 ∈ A, x = 5 ∈ A, x = 7 ∈ A, x = 9 ∈ A, x = 11 ∈ A do not satisfy x is an even number.

So the given statement is false, hence its truth value is F.

(v) Ǝ x ∈ A such that 3x + 8 > 40

Clearly x = 11 ∈ A and x = 12 ∈ A satisfies 3x + 8 > 40.

So the given statement is true, hence its truth value is T.

(vi) \(\forall\) x ∈ A, 2x + 9 > 14

For each x ∈ A,

2x + 9 > 14.

So the given statement is true, hence its truth value is T.