Relation and Function - NCERT Exemplar Problems and Solution (Short Answer Type)

Short Answer Type NCERT Exemplar Problems and Solution

Question – 1 Let$ A = (a, b, c)$ and the relation $R$  be defined on $A$  as follows:
$R = ((a, a), (b, c), (a, b)).$
Then, write minimum number of ordered pairs to be added in $R $ to make $ R$ reflexive and transitive.

Solution:

In order to make R reflexive,$ (b, b) $ and $(c, c) $ will be added to $R$

And in order to make $ R$  transitive,$ (a, c)$ will be added to $R.$

Therefore, The minimum number of order pair to be added to $R$ will be $(b, b), (c, c) $ and $ (a, c) $ ♦

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Long Answer Type NCERT Exemplar Problems and Solution Part 1

Question – 16: If $A = (1, 2, 3, 4)$, define relations on $A$ which have properties of being

(a) Reflexive, transitive but not symmetric

(b)  Symmetric but neither reflexive nor transitive.

(c)  Reflexive, symmetric and transitive.

Solution: Let $R_1 $= { $(1,1),(2,2),(1,2)$}

Thus, it is clear that $(1,1)\in R_1$ and $(2,2)\in R_1$

Thus $R_1$ is reflexive.

Again, $(1,2)\in R_1$ $but\hspace{5pt} (2,1)\notin R_1 $

Thus it is not symmetric.Now,  $(2,1) \in R_1, $ and $(1,1)\in R_1 $ $ \Rightarrow (2,1)\in R_1$ Thus $R_1$ is reflexive and transitive but not symmetric.

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