Question 1. Quick answer questions (a) Let S = {3, {5}, {7, 1}}. Are the following statements true or false? (i) {3,7} # S (ii) {7} € S (iii) {7, {1}}

Q: Express the following sets in the simplest way possible. If needed, use 'set builder notations'. Do…

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Q: 4. Write out the following sets, and give a formal proof that set-builder notation expression (as…

A: The set builder notation is given as, {x∈ℝ: x2=x} × {x∈ℕ : x2=x} As in the case of real numbers all…

Q: Give examples of the following, and provide justification as to why your answers are examples of the…

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Q: The Venn diagram here shows the cardinality of each set. Use this to find the cardinality of each…

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Q: Find the following cardinalities (Do not list the elements of the sets). A² = A x A, for any set A.)…

A: “Since you have asked multiple questions, we will solve the first question for you.If you want any…

Q: Identify the theorems and/or identities that justify each step in the derivation below. If A and B…

A: The objective of the question is choosing corresponding identity law and rule.

Q: Prove: |P(A)|= 2" where |A| = n. (Here P(A) is the power set of the set A with n elements.)

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Q: Identify all possible proper subset relationships that occur among the following sets. A = {3n + 1|n…

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Q: Let: A = {2, 4, 8} B= {1,2,3} C = {0, 1} What is the cardinality of: A x Bx C

A: The given sets areA={2, 4,8} ,B = {1,2,3} ,C = {0, 1}

Q: Write each set in the indicated form. If you need to use "..." to indicate a pattern, make sure to…

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Q: Trick Question: what is the cardinality of the following set A: A = {0, {}, {1}, {1, {2}}, {1, 1},…

A: Given that : A = {0, {}, {1},{1,{2}},{1,1},{3}}

Q: Given A = {3, 6, 9, 10, 12} and B = {1, 6, 9, 12}, find each of the following set cardinalities:…

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Q: A n(A) = 5 3 C 4 X 0³ 6 1 14 9 7 B 5

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Q: (b) Find the cardinalities of the following sets: A = {{, {3}}} (c) Write down the proper subsets of…

A: The given set is A=π, 3, B=∅, ∅. We have to find the cardinalities of the given sets. We have to…

Q: The counterexample of A = {1} and B = Ø disproves which of the following statements where P(X)…

A: Given that A=1,B=∅. For (a). PA∩B=P1,∅∩∅=P∅=∅ And, P(A)∩P(B)=P1∩P(∅)=1,∅∩∅=∅ Hence statement of (a)…

Q: (a) Suppose A and B are sets such that |A|≤|B|. Prove that P(A)| ≤ |P(B)|. (b) Suppose now that |A|…

A: (a) Suppose A and B are sets such that |A||B|. We have to Prove that P(A)| ≤ |P(B)|. (b) Suppose now…

Q: Write each of the following sets by listing its elements between braces and then find its…

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Q: Given three sets A, B, and C. A = {x €Z|-2<x<1},B= {x€Z]x2-1=0}, C= {0, – 1,- 2, -3}. (a) List…

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Q: For each of the following sets, decide whether it is finite, countable, or uncountable. Explain your…

A: Let  be any set , then

Q: (a). Show that (0, 1) × (0, 1) and (0, 1) have the same cardinality. (Hint: shuffling two digit…

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Q: Question 4. elements a, b, and c are distinct) Explain your answer. (a) Ø (b) {0, {a}} (c) {Ø, {a},…

A: The power set of a set S is the set of all subsets of S, including the empty set and S itself. In…

Q: w many different functions are there from a set with 10 elements to sets with 2 elements?

A: product rule : If one event can occur in m ways and a second event can occur in n ways ,the number…