5. Consider the operation a * b = |b|. a) Is this a binary operation on the set S = R? Justify your answer. b) Is this a binary operation on the set S = {–4,–3, –1, 1,2,3,4}? Justify your answer.

Q: (Assume that in a university with 1000 students. 200 students are taking a course in mathematics,…

A:

Q: (1) *, Let A and B be sets prove the following. (c) A C B if and only if B° C A°.

A: Let A and B be sets.

Q: Assume that * is a binary operation on a nonempty set A, and suppose that * is both commutative and…

A: Assume that * is a binary operation on a nonempty set A, and suppose that * is both commutative and…

Q: 5. Suppose that A is a set and {Bn}nɛ1 is an indexed family of sets. Prove that A - UB, = N(A – B,).…

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Q: Determine whether the set S = {1, x², 3 + x²} spans P2. O S spans P2. O s does not span P2.

A: Consider the given set S. S=1,x2,3+x2 Now, make the matrix from the given set. 103000011

Q: 4. Use set identities or different proof method to show that: (A U B) n (B U A°) = B

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Q: Let A1, A2,...,An, for n is amd element of natural numbers (N), be finite sets. Prove that |A1 x A2…

A: GIVEN : Let A1, A2,...,An, for n is and element of natural numbers (N) be finite sets.  TO PROVE :…

Q: Suppose that A and B are sets. Prove that A- B = AnB.

A: Suppose that A and B are set. Prove that A-B=A∩B¯.

Q: 9. Give a proof by contradiction to show if A and B are sets, then A N (BN A') = {}.

A: Suppose A and B are sets.

Q: 11. Use set identities or different proof method to show that: a) (B- A)U(C- A) = (BUC)- A b) (4 –…

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Q: Let A, B and C be sets such that Al = 17 |B= 10 C= 11 and the intersection of any two of these sets…

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Q: Determine whether the set S = {1, x², 6 + x²} spans P2. S spans P2. O s does not span P2.

A: P2 is the vector set of all polynomials with real coefficients of degree 2 or less. So 1+x is an…

Q: Let the universal set U = {x | x is a positive integer}. Also, let A = {x ∈ U | x is divisible by…

A: Given, U={x | x is a positive integer} The positive integers are  1, 2, 3, ... i.e. the natural…

Q: Suppose that each of A, B, and C is a set and each of BnC, A–(BnC), A-B, A-C, and (A – B) n (A – C)…

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Q: prove that i } X is a Coun table set and P: X>Y is asurjecbive then Y is Countable

A: Note: X denotes cardinality of X, that is number of elements in the set X. If X is countable means…

Q: Of the 70 students in Dr.Cross’s Math118 section, 40 can program in Randin Python, 30 can program in…

A: Given information: The total number of students in the class is n(T) = 70. The number of students…

Q: (4) Prove by contradiction, for any sets A and B, if ACA- B, then An B= Ø

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Q: Let S be a set of four elements given by S = {A, B, C, D} with the following table. * A B c D A B c…

A: If S be a set of four elements given by S = {A, B, C, D} with the following table. We have to show…

Q: Suppose A is a set having n elements. a. How many relations are there on 4? b. How many reflexive…

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Q: 4. (a) Write down four distinct elements of the set {2 €C:2- E = 2i}.

A: Note:  We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: 7. Consider the following table that displays the binary operation on the set {x,y,z). I N 8 (a)…

A: This is a question from abstract algebra.

Q: Prove for every two sets A and B that A∪B= (A-B)∪(B-A)∪(A∩B)

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Q: Assume that* is an associative binary operation on the nonempty set A. Prove that a* [b* (c*d)] =[a*…

A: We assume that * is an associative binary operation on the nonempty set A. Prove that a* [b* (c*d)]…

Q: If A is a countable set and B is an uncountable set, then the MOST we could ever say about A U Bis…

A: We have given the three MCQ questions about countability and uncountability . We have to choose the…

Q: 19. For all sets A, B, and C, if AC BandACC then AC BnC.

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Q: 1. Let A, B, and C be sets. Does A - B = A – C imply B = C? If so, prove it. If not, give a…

A: This question is related to Set theory, We will solve it using given information.

Q: Is ∗ defined on the set {1, 2, 3, 4, 5} by  a ∗ b = L.C.M. of a and b a binaryoperation? Justify…

A: Given:

Q: 2. Let S be the set of three elements given by S = {A, B, C} with the following table. * A B A A B B…

A: From the given table , we can see that  A*B=B= B*AA*C=C=C*AB*C=A=C*B So, the binary operation * is…

Q: D. Determine whether or not each of the following definitions of * given below does give a binary…

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Q: Let X = {a, b, c}, Y = {a, c, b}, and Z = {a, b, b, c, c, c}. What are the elements of X, Y, and Z?…

A: It is known that the ordering of the elements in a set does not matter. If the elements of both sets…

Q: D. Determine whether or not each of the following definitions of * given below does give a binary…

A: Solution of D part (1): (1) The set ℤ+ is ℤ+=1,2,3,... The operation * is defined as a*b=ab

Q: 3) If E={ students of a certain school },describe the complement of each of the following sets (…

A: We know that complement of a set A is the set of all elements which are not in the set A. (a)  Given…

Q: 22. Let 2 be a non-empty set and let C be all one point subsets. Show that o (C) = {A C 2 : A is…

A:

Q: 1. Are the two sets (An B)UC and A - (Bn C) the same set? Use Venn Diagram shadings to prove your…

A: As per our Bartleby guidelines, we are allowed to answer one question per query, Please ask Q2 as a…

Q: Which of the following sets are closed under multiplication?

A: Given: (a) The set of all prime numbers. (b) The set of all even numbers. (c) The set of all…

Q: For an element to be in the union of sets A and B, the element must be in set A in set B. but not…

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Q: Any binary operation defined on a set containing a a single element is commutative and associative.…

A: Every binary operation defined on a set having exactly one element is both commutative and…

Q: Let Σ = {0, 1, +, =} and S = {x = y+z : x,y,z ∈ {0,1}* and x,y,z are binary integers, and x is the…

A: Given that S=x=y+z By using the pumping lemma. Assume that for the purpose of reaching a…

Q: 2. (i) Show that given finitely many countable sets A1, A2,, An, the set A1 x A2 x .. x An is also…

A: A set A is said to be countable if its cardinality is same as the set of natural numbers ℕ. If A and…

Q: 1. Prove or Disprove: For all sets A and B, MUB- M+ B

A:

Q: (4) How many distinct pairs of disjoint non-empty subsets of A are there, the union of which is all…

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Q: Use the following outline to supply proofs for the statementsin Theorem 1.5.8.((i) If A1,A2, . . .…

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Q: 2. Draw a Venn diagram for the set AU(BnC).

A: We first draw U, A, B, C

Q: 2. Prove that by laws of set, (A - B)- (B - C) = A -B

A:

Q: Consider the relation = on the natural numbers 9...24. How many sets are in the partition of 9...24…

A: As we that '=' is the equivalence relation then we have a partition with the set of the natural from…

Q: 2. Consider the operation (*) defined on the set S = {1,2,3} by operation table :- 2 Show that the…

A: Given that the operation (*) defined on a set S = {1,2,3} then  the operation (*) is associative if…

Q: Which of the following is the correct representation of A = (2,4.8.16,32. in set puilder notation?"…

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