# Q. 15 Let R be the relation in the set $\{}1, 2, 3, 4\}$ given by $R = \{(1, 2), (2, 2), (1, 1), (4,4), (1, 3), (3, 3), (3, 2)\}$. Choose the correct answer.(A)  R is reflexive and symmetric but not transitive.(B) R is reflexive and transitive but not symmetric.(C) R is symmetric and transitive but not reflexive.(D) R is an equivalence relation.

A = $\{}1, 2, 3, 4\}$

$R = \{(1, 2), (2, 2), (1, 1), (4,4), (1, 3), (3, 3), (3, 2)\}$

For every  $a \in A$  there is  $(a,a) \in R$

$\therefore$ R is reflexive.

Given, $(1,2) \in R$  but  $(2,1) \notin R$

$\therefore$ R is not symmetric.

For  $a,b,c \in A$ there are $(a,b) \in R \, and \, (b,c) \in R$  $\Rightarrow$ $(a,c) \in R$

$\therefore$ R is transitive.

Hence, R  is reflexive and transitive but not symmetric.

The correct answer is option B.

## Related Chapters

### Preparation Products

##### Knockout NEET July 2020

An exhaustive E-learning program for the complete preparation of NEET..

₹ 15999/- ₹ 6999/-
##### Rank Booster NEET 2020

This course will help student to be better prepared and study in the right direction for NEET..

₹ 9999/- ₹ 4999/-
##### Knockout JEE Main July 2020

An exhaustive E-learning program for the complete preparation of JEE Main..

₹ 12999/- ₹ 6999/-
##### Test Series NEET July 2020

Take chapter-wise, subject-wise and Complete syllabus mock tests and get in depth analysis of your test..

₹ 4999/- ₹ 2999/-