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Please Solve R.D. Sharma class 12 Chapter relations Exercise 1.1 Question 10  Maths textbook Solution.

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Domain of R is x ∈ N where x∈\left \{ 1,2,3............20 \right \}and

range of R is y ∈ N where \left \{ 39,37,35,......3,1 \right \}

The relation having properties of being neither symmetric nor transitive nor reflexive.


A relation R on set A is

 Reflexive relation:

If (a, a) \in R for every a \in A

Symmetric relation:

If \left ( a,b \right )is true then \left (b,a\right ) is also true for every a \in A

Transitive relation:

\text { If }(a, b) \text { and }(b, c) \in R, \text { then }(a, c) \in R \text { for every } \mathrm{a}, \mathrm{b}, \mathrm{c} \in A


R=\{(x, y): x, y \in N, 2 x+y=41\}


The domain of R \text { is } x \in N, \text { such that } 2 x+y=41

x=(41-y) / 2

Since y \in N, largest value that x can take corresponds to the smallest value that y can take.

\therefore \quad x=\{1,2,3 \ldots .20\}

Range R of is  y \in Nsuch that


\begin{gathered} 2 x+y=41 \\ y=41-2 x \\ x=\{1,2,3 \ldots 20\} \end{gathered}

y=\{39,37,35, \ldots . .3,1\}

Since (2,2) \notin R, R,is not reflexive.

Also, since (1,39) \in R(39,1) \notin R, R is not symmetric.

Finally, since (15,11) \in R \text { and }(11,19) \in R \text { but }(15,19) \notin R, R is not transitive.



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