Let *' be defined on the set N. Which of the following are both commutative and associative?

Q: Use double set inclusion to prove that dep. PANB) = P(A)n P(B).

A: The problem is related with power set P of sets. Here, we have to show that P A ∩ B = P A ∩ PB using…

Q: 6. Consider the operation a * b = a + b² on the set S = Z. a) Is this operation commutative? Justify…

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Q: Z+ is the set of positive integers. Let A = {1,2,3), B = {n ∈ Z+ | n is even}, C = {n ∈ Z+ | n is…

A: concept Used: C∩D is the set  containing all elements of C that also in the set D C∪D is the set…

Q: Let U be the universal set and it contains all the positive integers less than 13. Let A and B be…

A: Solution: The given universal set is U=1,2,3,4,5,6,7,8,9,10,11,12 A is the set of positive integers…

Q: Give 3 different examples of norms on Z (set of integers)

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Q: Let X be the set comprising all numbers of the following two types: • Natural numbers; • Natural…

A: From (i) & (ii), we conclude that the function f is well defined.

Q: Prove that the following statement is a tautology (~q^(p⇒q)) ⇒~p

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Q: How many proper subsets are there of the set A = {Mallory, Janet, Kaitlynn, Akira}?

A: Given,         The set A= Mallory, Janet, Kaitlynn, Akira .

Q: Suppose A1, A2,... An are sets in some universal set U, and n ≥ 2. Prove that(A1 ∪ A2 ∪··· ∪ An)` =…

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Q: A = {x € Z: xis even} {91'SI'ZI'6'S'E} = 5 23242+3 2184 21+ 122198 th

A: Given,            To find the value of

Q: Insert either ⊆ or c/ in the blank space between the sets to make a true statement. {6, 8, 10, . .…

A: We can answer the question in the below steps.

Q: For any set S if a*b = b*a, Va, b e S then * is said to be on S. (A) closed (B) associative (C)…

A: (a) For any set S if a*b∈S , ∀a, b ∈S , then *is closed on S   (b) For any set S if a*(b*c) =…

Q: Is the following true or false? ∅ ∈ {∅,a}

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Q: Show that (B- A)U (C-A) = (BU C)- A 1) Using Venn diagrams 2) Using the set-builder notation and…

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Q: Vrite the belonging condition for the following set, using quantifiers A = {a³ + b³ + c³|a, b € R^c…

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