Let A = {0, 2, 4, 6, 8, 10}, B = {0, 1, 2, 3, 4, 5, 6}, and C = {4, 5, 6, 7, 8, 9, 10}. Prove the following; (A − B) − C = (A − C) − (B − C) A ∪ (B ∪ C) = (A ∪ B) ∪ C

Q: Suppose that A ⊆ B and x ∈ A. Use the method of “proof by contrapositive” to show that if x ∉ B - C,…

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Q: Let A, = [0, 2 + ±], for n = 1, 2, 3, 4, 5, . .. Find n U An and ( An ? n=1 n=1

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Q: Prove that if A ⊂ B and B ⊂ C, then A ⊂ C

A: Given problem is :   Prove that if A ⊂ B and B ⊂ C, then A ⊂ C.

Q: Prove that if A1,A2,…,An and B are sets, then (A1−B)∪(A2−B)∪⋯∪(An−B)=(A1∪ A2 ∪⋯∪ An)−B.

A: To Prove- Prove that if A1, A2, ...., An and B are sets, then A1 - B ∪ A2 - B ∪ .... ∪ An - B = A1 ∪…

Q: Show that if all A's are B's, and no B's are C's, then no A's are C's.

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Q: o sets are equal if and only if A=B b. ACB and BCA c. AcB and BCA d. ACB and BCA а.

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Q: 2. Prove that if a, b e R, then (a) -(a + b) = (-a) +(-b), (c) 1/(-a) = –(1/a), (b) (-a)·(-b) = a ·…

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Q: Prove that if r <s < n, then P(n , s) is divisible by P(n,r).

A: Given: r≤s≤n Therefore, n-r≥n-s So we can write n-r! = n-rn-r-1n-r-2...n-sn-s-1n-s-2...1 n-r! =…

Q: a) If A belongs to B and B belongs to C, then A belongs to C. b) If A belongs to B and B belongs to…

A: Solution

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

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Q: Prove that for all a, b, and c e Z, if a † (2bc+12), then a † (b – 2) or a ł (c + 3).

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Q: Prove that if A ⊂ C and A ⊆ B ⊆ C, then either A ⊂ B or B ⊂ C.

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Q: If any subset of size five is chosen from {1, -1, 2, -2, 4, -4, 8, -8), then prove that each of the…

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Q: Prove that, if (a%m)=(b%m) then m| (a-b)

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Q: If all fruit bearing plants are flowering plants, and all flowering plants attracti nsects. Which of…

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Q: Prove or disprove the following: (a) If B CC and B nA 6= Ø, then C nA 6= Ø. (b) If B CC and B nA =…

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Q: Prove that A(BC) = (AB)C.

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Q: Prove that if a|b and b|c, then a|c.

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Q: Let A = {1, 3, 5, 7}, B= {5, 6, 7, 8}, C= {5, 8}, D= {2, 5, 8}, and U= {1, 2, 3, 4, 5, 6, 7, 8}.…

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Q: 12. Prove: If AC B and C C D, then ANCCBND.

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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: (a) For all a, b, c e N, if abc > 27, then at least one of a, b, or c is greater than or equal to 3.…

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Q: 3. Let A, B, and C be sets. Prove or disprove that A- (BNC) = (A-B) U (A-C).

A: Solution

Q: Let A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and    B = { 2, 3, 5, 7 }. Find A ∩ B and hence show that A…

A: A ∩ B = {1,2,3,4,5,6,7,8,9,10} ∩ {2,3,5,7}           = {2,3,5,7}           = B

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

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Q: Let a, b, c be integers. Prove that if a|b and a|c, then a|(b +c).

A: Suppose a|b and a|c. Then there are integers m and n such thatb = am and c = an.Then b + c = am + an…

Q: Prove: If a &lt; 0 and b &gt; 0, then | a  + b | &lt; | a | + | b |

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Q: Let A={a;a=3n and nEN,ns4} ,then A in Roster form is {3,6,9,12}

A: Roster or tabular form: In roster form, all the elements of a set are listed, the elements are being…

Q: Prove: If A ∪ C = B and A ∪ D = B and A ∩ C = ∅ and A ∩ D = ∅, then C=D.

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Q: Prove or disprove that if (A U B) C (An B), then A = B

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Q: Suppose you were asked to prove the following theorem: For all sets, A and B, if AnB ¢, then A+ ø.…

A: Here we have to identify the hypothesis, conclusion and quantifier of the following theorem ''For…

Q: 1. Suppose A, B, and C are sets, A. Prove that: AX (Bn C) = (A X B) n (A x C) %3D

A: As per our guidelines we are supposed to answer only one question.Since you have asked multiple…

Q: if C={}         is {} subset of C ?

A: Question: Is the empty set a subset of itself?

Q: Let A={a; a=3n and nEN, ns4} ,then A in Roster form is {3,6,9,12}

A: To write the given set A in the Roster form, we use the definition of representation of a set in the…

Q: Let A = {{1} , Ø}, then O{Ø} C A, Ø CA O{Ø} Z A, Ø C A O{Ø} Z A, Ø L A O{Ø} C A, Ø L A

A: In this question we have to solve a set A.

Q: "x is in A"  and "x is in B"

A: " x is in A intersection B" is same as " x is in A" and " x is in B".  For "x is in A union B" is…

Q: Let A, b,, and b, be as defined below. 、目、 [1 2 -1 -2 2 0 2 3 -2 -3 4 0 A= |1 2 2 3 17 2 04 2 3 06…

A: As per bartleby guideline for more than three sub parts asked only first three are to be answered…

Q: Let a, b,c € R4. Prove that c+a a+b b+c c+b a +c b+a Al

A: a,b,c∈ℝ+ab+bc+ca≥c+ac+b+a+ba+c+b+cb+a

Q: Which of the following is NOT a subset of 2{a,b} × {a,b} C (b). Ø) C (a,b), (a,b) ) C (a,b}, a) C…

A: Given set

Q: 3. Let A, B, C, and D be sets. (a) Prove that (A × C) n (B × D) = (An B) × (Cn D).

A: Let A, B, C, and D be sets.To prove the equality, we have to show that, LHS is a subset of RHS and…

Q: Let A = {1, 3, 5, 7}, B= (5, 6, 7, 8), C= {5, 8}, D= (2, 5, 8}, and U=(1, 2, 3, 4, 5, 6, 7, 8}.…

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Q: How to solve this?

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Q: . Prove that is A < B and B < A, then A -

A: The relation defined in the above equation represents anti symmetry.

Q: a. If A and B are independent, and A and B are independent, show that A and B are also independent.

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Q: Show that for n attributes A1, A2, A3, ..., A, (Aj A2 Az ... A, ) 2( Aj ) + ( A2 ) + ( A3 ) + ... +…

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Q: Prove. 'if 0 < a ≤ b, then a2 ≤ b2 and √a ≤ √b.'

A: According to question,Given condition,0&lt;a≤b

Q: Let a, b, c, d ∈ Z. Prove the following statements. (a) If c | ab and (c, a) = d, then c | db; (b)…

A: (a) given  c|ab and c,a=d to show  c|db

Q: Prove that if p,q, and r are integers, r|p and r|q, then r^2|pq.

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Q: 4. Prove: Let a, b e Z*. If a|b and bla, then a = b or a = -b.

A: If a/b and b/a then prove that a=b , a=-b.

Q: Let S = {a, b,f,g, i, k, m, q, t} . (1) How many subset of S have exactly 3 elements? (2) How many…

A: We have to find no. Of subset as per given question.