Question

the number of non trivial relations on the set A=(a,b,c) is​

Answer 1

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

TO DETERMINE

The number of non trivial relations

on the set A= { a, b, c}

EVALUATION

Here A= { a, b, c}

So the number of elements in A = n (A) = 3

Now a relation from A to A is a subset of A × A

Here n ( A × A ) = n (A) × n (A) = 3× 3 = 9

Hence the number of relations from A to A is

$\sf{ = {2}^{9} \: }$

$= 512$

Also the trivial relations from A to A are

$\sf{ \Phi \: \: and \: \: A \times A}$

So the number of trivial relations from A to A is 2

Hence the number of non trivial relations on A is

$= 512 - 2$

$= 510$

━━━━━━━━━━━━━━━━

LEARN MORE FROM BRAINLY

Given set A = {1, 2, 3... 10}

Relation R is defined in set A as

R = {(a, b)€ A × A : a = 2b}

Then range of relation R is

Then range of relation R ishttps://brainly.in/question/23567484