Plz ans this .

Plz ans this . Two finite sets A and B have A and g elements respectively. The number of elements in the power set of the A is 224 more than the total number of elements in the power set of B. What is the number of relations from A to B?

Number of elements of set A=λNumber of elements of set B=μWe know that number of subsets of set A=2λWe know that number of subsets of set B=2μA.T.Q2λ=2μ+2242λ-2μ=2242μ2λ-μ-1=2523-1On comparing both sides ,we getμ=5 and λ-μ=3λ-5=3λ=8Now we know that A×B consists of λμ=8×5=40 ordered pairs  .So total number ofsubsets of A×B is 2λμ=240.Since each element of A×B defines  a relation from A to B.So total number of relations from A to B is  2λμ i.e. 240

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