Determine whether ⊂,⊆⊂,⊆ , both, or neither can be placed in each blank to make the statement true. ∅∅ _____  {0}   (a) ⊂⊂ (b) ⊆⊆ (c) both (d) neither Let U = {a, b, c, d, e, f, g} A = {a, e} B = {a, b, e, f, g} C = {b, f, g} D = {d, e} Determine if the following is True or False A ⊂⊂ B   (a) True (b) False Let U = {a, b, c, d, e, f, g} A = {a, e} B = {a, b, e, f, g} C = {b, f, g} D = {d, e} Determine if the following is True or False D ⊂⊂ B   (a) True (b) False

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Q: Sets A, B, and C are subsets of the universal set U. These sets are defined as follows. U={f,g,h,p,…

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Q: Extra Credit. Let A and B be (not necessarily finite) sets. Prove that if A = B, then P(A) × P(B).

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Q: Let A = ℤ , B = { n ∈ ℤ | 50 < x < 500 }, C = { n ∈ ℤ | 0 < x < 50 }, D = { 5, 10, 15, 20, 25, 30,…

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Q: Use an element argument to prove the statement. (Assume that all sets are subsets of a universal set…

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Q: For all sets A, B, and C, An (BU C) = (A N B) U (AN C). Fill in the blanks in the proof for the…

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Q: Let U = {a, b, c, d, e, f, g} A = {a, e} B = {a, b, e, f, g} C = {b, f, g} D = {d, e} Determine if…

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Q: Every set S has an open cover.

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Q: Xn (Y– Z) = (XnY) – (XnZ) -

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Q: Sets C and D are subsets of the universal set U. These sets are defined as follows. U = {m,r,x, y,…

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Q: Let A, B, U and V be any sets such that A⊆U and B⊆V. Is (A×B)⊆(U×V)? Justify your answer

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Q: niversal set, A = {x ∈U |P (x)}, and B = {x ∈U |Q(x)}, where P, Q are formulas such that (∀x ∈U )(P…

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Q: Let X = {a, b, c, d, e} and let T= {X, Ø, {a), {c,d}, {a,c,d}, {b,c,d,e} }, then O X T) is neither…

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Q: Homework: Determined whether the following sets are open or closed in (IR", ||. |I): 1) [a , b1] ×…

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Q: %3D Let C, D be subsets of a set U. By proving two inclusions, show that (CC n D) U (Cn D) = D where…

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Q: Sets B and D are subsets of the universal set These sets are defined as follows. U={f,k, m, q ,r, s,…

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Q: Use an element argument to prove the statement. (Assume that all sets are subsets of a universal set…

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Q: Let A and B be any two sets.prove that (A_B)U(B_A)=(A UB)_(AnB).

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Q: a) Let A, B, U and V be any sets such that A C U and B CV. Is (A x B) C (U x V)? Justify your…

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Q: 6. Use a direct proof technique to prove the following theorems: The sets A, B, and C are arbitrary…

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Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.