Question

If maximum number of relation on set A is 512, then find the cardinal number of A.​

Answer 1

Answer:

relation is subset of A X B so

Step-by-step explanation:

max no. of relation on set A is ( 2)^ m*n

total relation = 512

relation on set A itself = 512

512 = (2)^ 9

512 = (2) ^ 3*3

now set A has an element is 3

then n(A) = 3

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Answer 2

Answer:

The correct answer of this question is $2^{m . m} = 2^{9} = m^{2} = 9 = m = 3$.

Step-by-step explanation:

Given -  Maximum number of relation on set A is 512.

To Find - Find the cardinal number of A.​

set A has m elements and B has n elements, then there are $2^{mn}$ different relations from A to B.

And the relation from set A to A. Therefore, if the number of elements in set A (cardinal no ) is m then-

A number that shows the number of elements in an assemblage and is used in basic counting.

Total relations = $2^{m . m}$ = $512$

$2^{m . m} = 2^{9} = m^{2} = 9 = m = 3$

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