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=3⇒λ-5=3⇒λ=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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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 = λ Number of elements of set B = μ We know that number of subsets of set A = 2^{λ} We know that number of subsets of set B = 2^{μ} A . T . Q 2^{λ} = 2^{μ} + 224 2^{λ} - 2^{μ} = 224 2^{μ} (2^{λ - μ} - 1) = 2^{5} (2^{3} - 1) On comparing both sides, we get μ = 5 and λ - μ = 3 \Rightarrow λ - 5 = 3 \Rightarrow λ = 8 Now we know that A \times B consists of λμ (= 8 \times 5 = 40) ordered pairs . So total number of subsets of A \times B is 2^{λμ} (= 2^{40}) . Since each element of A \times B defines a relation from A to B . So total number of relations from A to B is 2^{λμ} i . e . 2^{40}

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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?

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?