Let R be a relation in the set N given by R = ((a, b) : a = b – 2, b > 6).

(a) (8, 7) € R:

To determine whether (8, 7) is in the relation R, we need to check if 8 = 7 – 2 and 7 > 6 are both true.

8 = 7 – 2 is true, but 7 > 6 is also true, so the ordered pair (8, 7) satisfies both conditions and is in the relation R. Therefore, (8, 7) € R is true.

(b) (6, 8) € R:

To determine whether (6, 8) is in the relation R, we need to check if 6 = 8 – 2 and 8 > 6 are both true.

6 = 8 – 2 is false, so the ordered pair (6, 8) does not satisfy the condition a = b – 2 and is not in the relation R. Therefore, (6, 8) € R is false.

(c) (3, 8) є R:

To determine whether (3, 8) is in the relation R, we need to check if 3 = 8 – 2 and 8 > 6 are both true.

3 = 8 – 2 is false, so the ordered pair (3, 8) does not satisfy the condition a = b – 2 and is not in the relation R. Therefore, (3, 8) є R is false.

(d) (2, 4) € R:

To determine whether (2, 4) is in the relation R, we need to check if 2 = 4 – 2 and 4 > 6 are both true.

2 = 4 – 2 is true, but 4 > 6 is false, so the ordered pair (2, 4) does not satisfy the condition b > 6 and is not in the relation R. Therefore, (2, 4) € R is false.