Let A, B, and C are three sets, prove that Bx(AUC)=(B× A)U(B×C)

Q: Prave that for all sets A and B, (ANB) = A UBC %3D

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Q: Let A, B, C, D be sets. Prove that (a) A × (BN C) = (A × B) N (A × C') (b) (A × B) N (C × D) = (AnC)…

A: Given (a) A×B∩C=A×B∩A×C (b) A×B∩C×D=A∩C×B∩D

Q: Let A=(1, 0), B=(0, 1), C=(1, 1), and D=(r, 1). Verify that R(A, B, C, D) = r.

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Q: For sets A and B, prove that AU (B – A) = B

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Q: Let A and B be sets. Prove that A U B = An B if and only if A = B

A: First show if A∪B=A∩B then A=B, then show that if A=B then we have A∪B=A∩B.

Q: Let B={(1,-2,1), (4,-7,5), (5,-8,8)], and x=(-6,10,-7) Find [x]B

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Q: Prove that (ab + cd)² ≤ (a² + c²)(b² + ď²) for all a, b, c, d ɛ R.

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Q: Ex. Show that [b, c) ~ [a, o), where a, b, c ER and b< c. [H7-9]

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Q: t U=(-5,9) be universal and set A=(-3,4)  B=(-1,6) , D=(0,8) Find the following: (i)(AnB)' (ii)BuD'

A: We can solve this question with the help of number line: Given set  U=(-5,9) A=(-3,4) B=(-1,6) And…

Q: Prove: For all sets A, B and C, (AUB) - (CA) = AU (B-C).

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Q: Let A, B, and C be sets. Prove (AUB)NC= (ANC) U(BNC)

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Q: Use direct prove to prove that for any two positive numbers x and y, x+y Vxy s 2

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Q: In cartesian product, prove that (A-B)XC=(AXC)-(BXC) A,B,C are sets

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Q: Define two operations + and * on A = Z × Z as follows: for (a, b) and (c, d) in A: ɔy (a, b)+(c, d)…

A: As per guidelines, we will solve first three subparts: Define two operations + and * on A=ℤ×ℤ as…

Q: Let U = {1,2,3,4,5), A={1,2,5}, B = {1,4,5), and C= {1,2,3}. (a) Find A U (BUC). (b) Find (A U B) U…

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Q: Exercise 2. Let A, B C R. (a) Prove that AUB = AUB. (b) Prove that ANBCAN B. (c) Find sets A and B…

A: Solution:-

Q: d) Suppose X = {1,2, 3} and Y = {5,6}. The number of elements of the set P(X× Y) =

A: Elements in X = 3. Elements in Y = 2 Elements in X × Y = 3 × 2 = 6

Q: {(r.0):3<rs4 and so<- Neatly sketch the set of points

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Q: df Catx) is expandad

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Q: Use any method you choose to shc are sets.

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Q: Let A, B, C, D be sets. (a) (b) Prove that Ax (B \ C') = (A × B) \ (A × C). Prove that (A x B) n (C…

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Q: Let G = (a, b | a² = b² = (ab)?). a. Express b²abab³ in the form b'a'. b. Express b'abab³a in the…

A: Given: The expression is G=a,b|a2=b2=(ab)2. To Express: (a) The expression b2abab3 in the form of…

Q: Let V be all elements of R2 that have the form (a, a2) where a is a real number. Show that (3,9) is…

A: Let V be all elements of R2 that have the form (a, a2) where a is a real number. We have show that…

Q: Prove than any pair of elements in H can be mapped to the positive y-axis by an element of SL(2, R).

A: According to the given information, it is required to prove that any pair of elements in H can be…

Q: Assume that A, B, C and D are sets. Verify that (A x B) U (C x D) ≤ (AUC) x (BUD).

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Q: y QI:: Let X₁, X₂ ~ N(0,1) 1) X1-X₂ X₁ + X2 2) (x1+x²)2 X₁-X2 what dist of 2X² 3) x² + x²

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Q: Is it true that (A×A)∖(B×B)=(A∖B)×(A∖B) for any two sets A, B? If it is true, prove it. Otherwise,…

A: Cartesian product and identity

Q: Give an example of four sets A, B, C and D such that (AUC) x (BUD) ≤ (A x B) U (C x D).

A: The set A is a subset of B if every element of A is in B

Q: 3. Let V be the set of all ordered triple in R³, and F, the set of real numbers, where the…

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Q: Prove: For all sets A, B and C, An (B-C) = (ANB) - (ANC).

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Q: Let X = {1, 2, 3, 4, 5} and Y = {7, 11, 13} %D are two sets. find R = {(x, y): x EX and * y EY and…

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Q: Prove that {4a + 126 : a, b E Z} = {4c: c € Z}.

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Q: If A and B are distinct points in 3-space then |AB| = - Select one: True False

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Q: Let A={2,y,z} and B={3,x,z}. How many distinct elements are in (A×B)∩(B×A)

A: Given, A={2,y,z} B={3,x,z} How many distinct elements are in (A×B)∩(B×A) ?

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.