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: ove that if AB = 1, then B = A- 2, 1 -1 21 and (b) 3 1 1 1 -2 1 2.

A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: Show that if a|b then -a|b.

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Q: Let  U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, a, b, c, d, e}.  If  A = {1, 2, a, e}  and  B =…

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Q: 1. Let U = {ab, bc, cd, de, ef, fg,gh, hi, if, jk} A = {cd, de, ef,fg} B = {ab, bc, cd, de} C = {bc,…

A: We have to solve

Q: Let A = {c, d, f, g} B = {f, j} C= { d, g} True or False: C C A? True False

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Q: Find u − v, 2(u + 3v), and 2v − u. u =  (6, −7, 8, 3),       v = (−2, , 7/3, −8/3 , −1)

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Q: Human blood can contain the A antigen, the B antigen, both the A and B antigens, or neither antigen.…

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Q: Show that if a\b and gcd(b, c) = 1 Then gcd(a,c) = 1 %3D

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Q: If (2,0),(0,1),(4,5) and (0,c) are concyclic, and then find c

A: If (2,0),(0,1),(4,5) and (0,c) are concyclic, and then find c

Q: I, \B|, A + B, and |A + B|. Then verify -1 1 8. 1 0 1 A = 0 1 1 B = -1 1 8 1 1 -1 0 1 8

A: Given: A=-11801111-1, B=101-118018

Q: Let a = (1,2, 3), b = (1,0, –1) and c = (2, 1, 3). (a) Verify that a · (2 b+c) =2(a · b) + (a · c).

A: a=(1,2,3) , b=(1,0,-1) and c=(2,1,3)

Q: Show that if A ⊂ B, then C – B ⊂ C – A.

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Q: (a-b)’ (b-c)' P (-9) a 3 d

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Q: space. O {A, B, C} О А, АВ, АС, ВА, В, ВС, СА, СВ, С) O (AB, AC, BA, BC, CA, CB} O {AA, AB, AC, BB,…

A: Two MCQseach MCQ have 3 choices A,B,Coutcomes in sum space=?

Q: Disprove by Contradiction If a,b,c ∈ ℕ, then at least one of a-b, a+c and b-c is even.

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Q: We know that P₁ = P2 on B if P₁ = P2 on C, provided that C generates B and is a 7-system. Show this…

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Q: Determine whether A=​B, A ⊆ ​B, B ⊆ ​A, A ⊂ ​B, B ⊂ ​A, or if none of these applies.…

A: Subsets are a part of one of the mathematical concepts called Sets.  In set theory, a subset is…

Q: If n/(a – b) and lcm(2b, 2n) = 2, then gcd(2a, 2n) = %3D %3D

A: We have to find the gcd of the two numbers   gcd= greatest common divisor the two numbers are 2a…

Q: (a) Show that if (a,342) = 171 and (b, 342) = 171 then (a+b,342) = 342. %3D %3D (b) Show that if (a,…

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Q: : let u (1, 2, 3), v = (2, 2, -1) and w = (4, 0, -4) then u-v + 2w equal %3D (7, 0, 1) O None O…

A: Calculate u-v+2w:  u-v+2w=1,2,3-2,2,-1+24,0,-4                  =1-2+2·4,2-2+2·0,3--1+2·-4…

Q: Let A = {1,2,3} and let R= {(1,1), (2, 2), (3, 3), (1, 2), (2, 1), (3, 2)} C A x A. In each case,…

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Q: (а) Ri: {(а, a), (b, b), (с, с), (а, d), (а, b), (b, а), (ь, с), (с, b)};B Circle : Reflexive…

A: I have circle the relations

Q: In Exercises 28-31, find proj,,v and proj, u. 28. u = (1, 4), v = (2, –3) 29. и 3D (3, —4), v %3D…

A: Disclaimer: "Since you have asked multiple questions, we will solve the first question for you. If…

Q: Let U = {a, b, c, d, e, f, g, h, i, j, k}. Let A = {c, d, f, g, i, j}. Let B = {c, e, g, i, j}. Let…

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Q: 10.

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Q: If z,,z,€C then Zz=Z2 OZi+Z2=Z,+z2 OZi+z2=0 Z,Z2=0=Z,=0 or zz=0

A: 2nd and 4th options are correct.

Q: If A ⊂ B, can A and B be independent under any circumstances? Explain

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Q: Let a = (1, 3, 8) and b = (7, 3, 4). Compute 5a + 7b

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Q: If a = qb +r. then gcd(a, b) = gcd(a,r).

A: In this question, we have to check the gdc(a,b)=gdc(a,r) if a=qb+r

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: 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}. Find a)…

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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 v = ⟨−1,3⟩. Draw v, −2v, and 3v in standard position.

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Q: Let  U = {1, 2, 3, 4, 5, 6, 7, a, b, c, d, e}.  If  A = {1, 2, a, e}  and  B = {1, 2, 3, 4, a, b,…

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Q: Le Let n=Layb,e, E, h, IJr B=(a,C,e,g)and b) BnC gAnc d AnBnc le)auB. Buc 9 AUC B.

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Q: Let u = (4, - 2), v = (-2,9), and w= (0, - 3). Express 8u - 5v + w in the form (a,b). !! ..... 8u -…

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Q: whether it is transitive. a) {(2, 2), (2, 3), (2, 4), (3, 2), (3, 3), (3, 4)} b) {(1, 1), (1, 2),…

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Q: If A and B are n × n and A + B is symmetric, then A and B are symmetric.  True or False...provide a…

A: If A and B are n × n and A + B is symmetric, then A and B are symmetric.

Q: Let A = 1 2 1 and v = If the entries of A and v belong to Z3, what is the third entry of Av? Answer:

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Q: Prove rem (a+b,c) = [rem(a,c) + rem(b,c)] , c

A: Note: rema,b=the remainder when a is divided by b. Then, by the quotient remainder theorem, there…

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: 1. For A = {1, 2, 3} and B = {3,4,5}, list all elements in A UB, ANB and A- B. o(b %3D

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: in how many ways can the numbers 1,2,3,4,5,6,7 be arranged so that  a. 1 and 7 are adjacent? b. 1…

A: a) If 1 and 7 are adjacent then we consider 1,7 as one number.  It can be 17 or 71. 2 ways. When 1,7…

Q: linear algebra, 2.5 question 5

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Q: 3. Show that if (AB)₁, (αB)₁, (Aß)₁, (αß)., and (AB)2, (αB)2, (AB)2, (aß)2, be two aggregates…

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Q: Let z, =1-1, z, =-2+4/, and z, = 3-21. Find Im().

A: Multiply z1 and z2 then divide by z3 then solve and get imaginary part

Q: Explain why the set is not a Basis. S = {(2,3), (6,9)}

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Q: Let a1 , az , .. , a7 e N. Show that if a¡ , a2, 7| (a, + az + ... + a7) .... 2.. a7 are…

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Q: Let A = (1,2), B= (1,3,4) C= (2,3,4) and U = (1,2,3,4,5), then (AU B) %3D %3D

A: FIRST WE WILL FIND A UNION B TRHEN WE WILL FIND ITS COMPLEMENT

Q: Find the generalized union and intersection: 1. A = {1,2,3,...} 2+1 Q-(무)

A: Let us find the generalized union and intersection of the given indexed set in the next step.

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”.