Class 12 Mathematics - Chapter Relations and Functions NCERT Solutions | Let R be the relation in the set N given
Let R be the relation in the set N given by R = {(a, b): a = b − 2, b > 6}. Choose the correct answer.
(A) (2, 4) ∈ R
(B) (3, 8) ∈R
(C) (6, 8) ∈R
(D) (8, 7) ∈ R
R = {(a, b): a = b − 2, b > 6}
Now, since b > 6, (2, 4) ∉ R
Also, as 3 ≠ 8 − 2, (3, 8) ∉ R
And, as 8 ≠ 7 − 2
∴(8, 7) ∉ R
Now, consider (6, 8).
We have 8 > 6 and also, 6 = 8 − 2.
∴(6, 8) ∈ R
The correct answer is C.
More Questions From Class 12 Mathematics - Chapter Relations and Functions
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(ii) Transitive but neither reflexive nor symmetric.
(iii) Reflexive and symmetric but not transitive.
(iv) Reflexive and transitive but not symmetric.
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(b) R = {(x, y): x and y live in the same locality}
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- Q:- Show that the relation R in R defined as R = {(a, b): a ≤ b}, is reflexive and transitive but not symmetric.
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