Number of relation from A to A which are both reflexive and symmetric is

Open in App

Solution

A relation has ordered pairs $(a, b) .$ Reflexive and symmetric Relations means $(a, a)$ is included in $R$ and $(a, b) (b, a)$ pairs can be included or not. (In Symmetric relation for pair $(a, b) (b, a)$ (considered as a pair). whether it is included in relation or not) So total number of Reflexive and symmetric Relations is $2^{\frac{n^{2} - n}{2}}$

Suggest Corrections

Similar questions

R

x R y ⟺ x - y + \sqrt{2}

R

x

y,

R

x R y \Leftrightarrow x - y + \sqrt{2}

R

Let A={1,2,3}. Then, the number of relation containing (1,2) and (1,3) which are reflexive and symmetric but not transitive is
(a)1
(b)2
(c)3
(d)4

A = {1, 2, 3}

(1, 2)

(1, 3)

Join BYJU'S Learning Program