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Finite and Infinite Set

Let Z be the ...

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Let Z be the set of all integers and A = {(x, y); x4y4 = 175, x, y E Z} B = {(x, y); xy, x, y EZ} Then, the number of elements in An B is

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X

be a set containing

6

P (X)

be its power set. The sets

A

B

are picked from

P (X) .

n (A) = n (B)

A \neq B,

then total number of ordered pair

(A, B)

: n (A)

represents number of elements in set

A

]

Z

denotes the set of all integers and

A = {(a, b) : a^{2} + 3 b^{2} = 28, a, b \in Z}

B = {(a, b) : a < b, a, b \in Z}

. Then, the number of elements in

A \cap B

Q. If X is a finite set. Let

P (X)

denote the set of all subsets of X and let

n (X)

denote the number of elements in X. If for two finite subsets

A, B, n (P (A)) = n (P (B)) + 15

n (B) =

n (A) =

Q. If X is a finite set. Let P(X) denote the set of all subsets of X and let n(X) denote the number of elements in X. If for two finite subsets A, B, n(P(A)) = n(P(B)) + 15 then n(B) = and n(A) =

Q. If A is a finite set, let P(A) denote the set of all subsets of A and n(A) denote the number of elements in A. If for two finite sets X and Y,

n [P (X)] = n [P (Y)] + 15

then find n(X) and n(Y).

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