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Question
Let R be relation defined on the set of natural number N as follows:
R = {(x, y): x ∈N, y ∈N, 2x + y = 41}. Find the domain and range of the relation R. Also verify whether R is reflexive, symmetric and transitive
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Solution
Given function: R = {(x, y): x ∈ N, y ∈ N, 2x + y = 41}.
So, the domain = {1, 2, 3, ….., 20} ......[Since, y ∈ N ]
Finding the range, we have
R = {(1, 39), (2, 37), (3, 35), …., (19, 3), (20, 1)}
Thus, Range of the function = {1, 3, 5, ….., 39}
R is not reflexive as (2, 2) ∉ R as 2 × 2 + 2 ≠ 41
Also, R is not symmetric as (1, 39) ∈ R but (39, 1) ∉ R
Further R is not transitive as (11, 19) ∉ R, (19, 3) ∉ R; but (11, 3) ∉ R.
Thus, R is neither reflexive nor symmetric and nor transitive.
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