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Question

Mathematics Question on Relations and Functions

Let R be the relation in the set N given by R={(a,b):a=b−2,b>6(a,b):a=b−2,b>6}.Choose the correct answer

A

(2,4)∈R(2,4)∈ R

B

(3,8)∈R(3,8)∈R

C

(6,8)∈R(6,8)∈R

D

(8,7)∈R(8,7)∈R

Answer

(6,8)∈R(6,8)∈R

Explanation

Solution

R=(a,b):a=b−2,b>6R = {(a, b): a = b − 2, b > 6}
Now, since b>6,(2,4)∉Rb > 6, (2, 4) ∉ R
Also, as 3≠8−2,(3,8)∉R3 ≠ 8 − 2, (3, 8) ∉ R
And, as 8≠7−2(8,7)∉R≠ 7 − 2 (8, 7) ∉ R
Now, consider (6,8).(6, 8). We have 8>68 > 6
and also, 6=8−2.∴(6,8)∈R6 = 8 − 2. ∴(6, 8) ∈ R

The correct answer is C.