Example: If A = {1, 2, 3,4,5}, B = {1, 2,4}, C = {2, 3,5}, verify that, A×(B∩C) = (A×B)∩(A×C)

Q: Give the dual of the following L. P. P. Max. : z = 2x1 + 3x2 + xXz Subject to : 4x + 3x2 + x3 = 6 X…

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Q: Show that if A × B = B × A then A = B

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Q: Let U = {h, i, j, k, I, m, n, o, p} A = {h, i, j, m} B= {h, k, I, m, o}

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Q: If a = (4, 0, 4), b = (3, 4,-4), and c = (0, 4, 5), show that a x (b x c) = (a x b) x c. 60i + 96j -…

A: Solution: Step-1                         Given if a = 4, 0, 4 ,b = 3, 4, -4, and c = 0, 4, 5, show…

Q: 15. Prove: If a, b, c, a, and M are constants and M = 0 then ax²y" + bxy' + cy has a particular…

A: Let us solve above problems.

Q: The set {[1 -1 3], [2 3 -2], [3 2 1], [0 0 0]} spans صواب İhi

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Q: Use z = a + bi and w = c + di to show that z + w =7 + W.

A: Consider a complex number z=a+bi Then, the complex conjugate of above complex number is given by:…

Q: Q. 02: (a) Verify the commutative propernties of union and Intersection with help of A = (1,2,3,4),…

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Q: Prove the following in axiomatic system. (A- (-B - C),~B}-A-C

A: Laws of inference are very useful in proving mathematical statements. We can build a sequence of…

Q: -2 23 3 in span Is {} 2 3 1 1

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Q: let a1 is (-3,2,6) a2 is (-9,-7,-2) and b is (-18,-27,-23). Is b in the span of of a1 and a2

A: The objective of this question is to determine whether the vector b is in the span of vectors a1 and…

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: 2. Using the fact that (AB)¹ = B-¹A¹, show that (ABC)¹ = C-¹B-¹A-¹.

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Q: \f a,b and C. are 10 Lhen 2०-30)

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Q: Compute 1 $ Jzmi\mu (22 +4)24z

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Q: If possible, Find AB and BA 4 A= (1, B= [3 -5 ]

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Q: Assume x and y are Boolean variables. What is the result of x+xy equals ?

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Q: Evaluate (p v q v -r) ^ (p v ¬q v ¬s) ^ (p v ¬r v ¬s) ^ (¬p v ¬q v ¬s) ^ (p v q v ¬s). O…

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Q: Suppose u=⟨−4,4,−2⟩ and v=⟨4,−2,3⟩. Then u×v=   v×u=

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Q: iken that I+2=1 xpressyin terms of xand z.

A: A function defines a relationship between two sets, where one set is dependent on other set. Any…

Q: compute A + B

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Q: -1- 3 5

A: Topic = Algebra

Q: Find, if possible, A + B, A- B, 2A, 2A- B, and B + A = 5-6 2 3 -4 1 (a) A + B 183 11 (b) A - B 188…

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Q: TRUE or FALSE: A\B = A when A and B are disjoint

A: Given statement ,A|B=A then A and B are disjoint

Q: Let A = {j, z}, B = {1,5,7}. Each element is expressed as an ordered pair. ВХА3{ }

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Q: 4) Which expression is equivalent to 1&r-50? 1) 2(3x + 5)² 2) 2(3х - 5)2 3) 2(3х - 5)(3х + 5) 4)…

A: we have to identify which expression is equivalent to the given expression

Q: 100 If A* = a + bi, compute for a and b.

A: To compute and a and b.

Q: -2 3 If A = Then, A-1 = %3D -6 4 4 2 a) 최 ( 6 3) 4 -2 b) – 6. 3 4 c) 24 6 -3 d) The inverse is not…

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Q: What is the Cartesian Product of A = {1,2} and B = {a,b}? Find AxB.

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Q: Find Jul, Ivl, 12u[, , lu + vl, lu - vl, and Jul - Ivl. u - (1, -4), v= (-10, –10)

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Q: Find the dual of the statement (xy¯¯¯)+(x¯¯¯z)

A: To find the dual of statement , we replace • by + and + by •

Q: find AB, BA, A +B, A - B, A, B, 5A, 3B. Observe that AB + BA. Show that (A - B)(A + B) # (A + B)(A –…

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Q: How do we know that -1 and -2 will be in the field?

A: Given F is field, So,  0, 1∈F ( since a field F must contain zero element and unity ) A field is…

Q: If ~v = 〈 4, 1, 6〉 and ~w = 〈3, 2, 3〉, find ~v · ~w and ~v × ~w.

A: If ~v = 〈 4, 1, 6〉 and ~w = 〈3, 2, 3〉, find ~v · ~w and ~v × ~w.

Q: В Calculate A and B so that + %D 1+x 1-

A:

Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.