For a given set S, let P(S) be the collection of all subsets of S. Let binary operations + and on P(S) be defined by A+ B = (AUB) - (An B) and A B = AnB for A, BE P(S). ... (d) Prove or disprove that P({z. y}, +,) is an integral domain. (e) Prove or disprove that P({r, y},+.) is a field.

Q: Prove that P(XY) = P(X)n P(Y) for all sets X and Y.

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Q: If A+ iB is Hermitian (A and Bare real) show that [ AB -BA] is symmetric.

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Q: use Gauss Fordanmetrecd to Solbe the fellowsing setafeg Qe linear 2X+ -4x2 +6X3=5 A +3X2-783=; + 5…

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Q: (b) Let {Ai e I}. Prove that 4) =UA;. |A, iel

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Q: Prove that B = (0,1) is NOT a compact set.

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Q: Show that R is not compact.

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Q: Let there be set of a, b, c. Prove A×(B∩C) = (A∩B)×(B∩C)

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Q: C. Let T be defined onN N by (a, b)T (c, d) if and only if a c and b 2 d. Write down the full nature…

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Q: 2) Let R real numbers, define = x,Y1 +4x2y2 + 6x3Y3 for x = (x1,x2, X3) and y (y1,y2, Ya). Is inner…

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Q: (5) Let ƒ : A → B and g : B → C, where f and g are functions and A, B, and C are sets. (a) Prove…

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Q: Let G = (-1,1) and (x,y) --> x ○ y = x + y/1 + xy is a binary operation on G. Let R+ = (0, ∞), with…

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Q: 1. Let 1 -0-0-0-0 = = = (a) (5 points) Find a orthonormal set {q1, 92, 93, 94} such that span{a₁,…

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Q: Prove that homotopy with respect to a domain 2 is a transitive property.

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Q: Show that U(8) is not isomorphic to U(10).

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Q: There are 16 binary relations on the set {0, 1}: (a) { } (d) {(1,0)} (g) {(0, 0), (1, 0)} (1) {(0,…

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Q: Let G = Z, O Z, H = {(0, 0), (2, 0), (0, 2), (2, 2)}, and K = ((1, 2)). Is GIH isomorphic to Z, or…

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Q: If f is a bijection of A onto B, show that f-1 is a bijection of B onto A.

A: Since  is a bijection from  onto , the inverse  is a bijection from .