Prove the following statements. a. Let a, b, c E Z. If a/b then abc. b. Let a, b € Z. If ab and a/c then a[(b+c). c. Let a, b € Z. If alb and bc then alc.

Q: B. Evaluate each. 1. C(8,4) 5. C(8,4) C(7,5) 22. C(5,0) 3. C(4,4) 4. C(11,3) C(7,4) 6. C(8,2) C(6,2)…

A: As per the guideline I’m supposed to solve only three sub-parts of the given problems.As we know…

Q: 10. Let A, B, and C be sets. Use the identities to show that (A U B) n (B U C) n (A U C) = Ā n Bn T.

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Q: 2. Which of the following operations is associative on Z? A. a*b = a b C. a*b = a B. a*b = max (a,…

A: Note: As per Bartleby guidelines if a question have more than 3 subparts and specific part is not…

Q: = [a b] and B =[2³]. a. Compute AB. b. If AB = 1-5₂ 1. Let A = find the entries of A, i.e. find the…

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Q: For every two sets A and B, if A–B = B – A , then A-B=Ø. For every two sets A and B, ANBCA-B.

A: (4) Given A and B are two set such that A-B=B-A for every A and B We have to show that A-B=∅ Now,…

Q: Let U, A, and B be defined as shown below. U ={a, b, c, d, e, f, g, h, i, j } A = { c, d, e, g, i} B…

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Q: Prove that if A – B – D and B – C – D, then A -C– D.

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Q: 7. Let B = AT A. Show that bij = a/aj.

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Q: Ema thinks that (u) xw, exists. Paul disagrees with her. Who is right? Explain why.

A: Dot product gives a scalar value  .

Q: a. Let a Z, then a² - 5a +7 is odd.

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Q: Which statement is an example of a transitive relationship? If x = 2y and 2y = 8, then x = 4. If clm…

A: Transitive relationship is a relationship in which if from the first two condition 3rd condition can…

Q: 2-2x set the gaplis. ffa)yaxl mxes sketh anad the iversé Dn uthe Same. End. expesso f fta An. ...i

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Q: Suppose a, b, c, d e Z, a + b = c, and dla. Prove that d|b if and only if d|c. 5.

A: see below the calculation steps

Q: Write the set containing two females in terms of A and B.   e. List the elements in !A, AB, AuB…

A: According to the given information, S=JD, JM, JS, JN, DM, DS, DN , MS, MN, SN A=JM, JS, JN, DM, DS,…

Q: Let a, b, c E Z. show that ca & cb if and only if c (a, b).

A: Division properties are used to prove it

Q: Let S {a, o, k, {a, b, c}}.Select the statements that are true. {a, o, k} E S a C S Ø ES {0} C S {o,…

A: The objective is to determine which of the giving statements are true. Given: S={a, o, k,{a, b, c}}.

Q: T T T T F 18. Let A and B be sets then A + B if, and only if A ¢ B and B ¢ A. For sets A, B, and C,…

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