Question

2) If n (A) = 3, n(B) =2, then number of non- empty relations from set A to set B are​

Answer 1

Answer:

Let n(A) = m, and n(B) = n. Then the total number of non-empty relations that can be defined from A to B is

(a) mn

(b) nm– 1

(c) mn – 1

(d) 2mn– 1

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1 Answer

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answered Feb 17, 2018 by nikita74 (-1,017 points)

d) We have, n(A) = m and n(B) = n

n(A xB) = n(A). n(B) = mn

Total number of relation from A to B = Number of subsets of AxB = 2mn

So, total number of non-empty relations = 2mn – 1

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Answer 2

Given: $n(A) = m$and $n(B) = n$

To find: number of non- empty relations from set A to set B.

Solution:

Find $\[n\left( {A \times B} \right)\]$.

$\[\begin{array}{l}n\left( {A \times B} \right) = n\left( A \right).n\left( B \right)\\ \Rightarrow n\left( {A \times B} \right) = mn\end{array}\]$

Find the total number of relation from A to B

Total number of relation from A to B $=$ Number of subsets of$\[A{\rm{ }} \times B{\rm{ }} = {\rm{ }}2mn\]$

Therefore,

total number of non-empty relations$\[ = 2mn - 1\]$.