Let R be relation defined on the set of natural number N as follows- R - x - y - x - N - 2 x - y -41- Find the domain and range of the relationR- Also verify whether R is reflexive- symmetric and transitive-

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Evaluation of a Determinant

Let R be rela...

Question

Let R be relation defined on the set of natural number N as follows, $R = {(x, y) : x \in N, 2 x + y = 41}$ , Find the domain and range of the relation R. Also verify whether R is reflexive, symmetric and transitive.

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Solution

Given that, $R = {(x, y) : x \in N, y \in N, 2 x + y = 41}$ .
Domain={1,2,3,....,20}
Range ={1,3,5,7,....39}

R={(1,39),(2,37),(3,35),....(19,3),(20,1)}
R is not reflexive as $(2, 2) / \in R$
$i . e . 2 \times 2 + 2 \neq 41$

As $(1, 39) \in R b u t (39, 1) / \in R$
So, R is not symmetric

As $(11, 19) \in R, (19, 3) \in R b u t (11, 3) / \in R$

Hence, R is neither reflexive. nor symmetric and nor transitive.

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Let R be relation defined on the set of natural number N as follows, R={(x,y):x∈N,2x+y=41}, Find the domain and range of the relation R. Also verify whether R is reflexive, symmetric and transitive.

Let R be relation defined on the set of natural number N as follows, $R = {(x, y) : x \in N, 2 x + y = 41}$ , Find the domain and range of the relation R. Also verify whether R is reflexive, symmetric and transitive.