Let U = {a, b, c, d, e, f, g} A = {a, e} B = {a, b, e, f, g} C = {b, f, g} D = {d, e} Determine if the following is True or False D⊆⊆ B   (a) True (b) False Let U = {a, b, c, d, e, f, g} A = {a, e} B = {a, b, e, f, g} C = {b, f, g} D = {d, e} Determine if the following is True or False B⊆⊆ C   (a) True (b) False Let U = {a, b, c, d, e, f, g} A = {a, e} B = {a, b, e, f, g} C = {b, f, g} D = {d, e}   Determine if the following is True or False: ACAC={b, c, d, f, g}   (a) True (b) False

Q: if A ={x,{y},1,2,3,{2,3},{3}}      {} a proper subset of A      true or false

A: The problem is concerned with the nature of the empty set. The specific question is whether the…

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

A:

Q: {(x,a),(x,b),(x,c), (y,a),(y,b),(y,c)} is the Cartesian product AXB of two sets given as A = {x,y} B…

A: Let A and B are two sets. Cartesian product of A and B will be denoted by  A×B                A×B…

Q: 2. Let U= { 11, 12, 13, 14, 15, 16, 17, 18, 19} and A = {12, 14, 16, 18} , B = {12, 15, 16, 19}, and…

A: A∩B={ Memberes in both A and B}A∩B={12, 16}

Q: Let X={a, b, c, d, e} and let T={X, non zero, {a}, {a, d}, {a, e}, then (X, T) is neither Hausdorff…

A:

Q: In Exercise 22, let u = PQ\ and v = PR\ , and find (a) the component forms of u and v, (b) u ∙ v,…

A: a) Answer(a): u=(-2,6,-2) and v=(3,6,-3)

Q: Let U={a, b, c, d, e, f, g, h, i, j}; A={a, c, e, g, i); B={a, c, i, j}; and C={f, g, h, i, j). List…

A: It is given that,   U = {a, b, c, d, e, f, g, h, i, j}   A = {a, c, e, g, i}   B = {a, c, i, j}   C…

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

A: i) Answer(i) A × (B ∩ C) = (A × B) ∩ (A × C) (proved)

Q: Let U={a,b,c,d,e,f,g,h,k}, A={a,b,c,g}, B={d,e,f,g}, C={a,c,f} and D={f,h,k} 1. Compute: a.) A U B…

A:

Q: Let X = {a, b, c, d, e} and let T= {X, ø, {a}, {c,d}, {a,c,d}, {b,c,d,e}}, then * (X, T) is not…

A: Option 2 is correct.

Q: Let S = {(1, 0, i), (1, 2, 1)} in C3. Compute S⊥.

A: For the given space in C3 let the desired perpendicular space be (a,b,c). It follows the conditions…

Q: If ZH and LJ are supplementary in HJKL, are a) ZK and ZL necessarily supplementary also? b) ZH and…

A: Given :∠H and ∠J are supplementary…

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A:

Q: Disprove the following statement by finding a counterexample. For all sets A, B, and 6, C, An (BUC)…

A:

Q: Let U = {1, 2, 3, 4, 5, 6}, A = {2, 3} and    B = {3, 4, 5}. Find A′, B′ , A′ ∩ B′, A ∪ B and hence…

A: Given: Now, The set of all those elements of U which do not belongs to A is called the complement…

Q: Are na V Independen O No, f(u,v) + fulu)fy(v) O Yes, f(u,v) = fulu)fy(v) No, f(u,v) = fu(u)fy(v) O…

A: It is given that f(u,v)=4uv.

Q: Let X = {a, b, c, d,e} and let T = {X, Ø, {a}, {a,d}, {a,e}}, then * O (X,T) is not connected but it…

A: No information is given for topology on Y So i have solved only the middle question

Q: Let: U = (a, b, c, d, e, f, g, h, i} A = {a, c, d, f, g, h} B = {b, c, d, e, i} Find (A U B). O (a,…

A: Given that,U=a, b, c, d, e, f, g, h, iA=a, c, d, f, g, hB=b, c, d, e, iThe set A∪B' is determined as…

Q: 9. If (X, M, u) is a measure space and E, FEM, then u(E)+μ(F) = μ(EUF)+ μ(EnF).

A: Introduction: A measurable function is a function between the underlying sets of two measurable…

Q: Prove logically that " C, + "C, + "C, + …· +"C, = 2".

A:

Q: Let U={a,b,c,d,e,f,g,h,k}, A={a,b,c,g}, B={d,e,f,g}, C={a,c,f} and D={f,h,k} 1. Compute: a.) A UB…

A: To evaluate the given set operations.

Q: Prove or disprove that if {a,} and {b,} are Cauchy and b,n # 0. Then An is Cauchy

A: If an and bn are Cauchy and bn≠0, then anbn is not Cauchy. Result used: If an and bn are Cauchy and…

Q: Select the law that establishes that the two sets below are equal: Gn (GU Z) = G OAbsorption Law O…

A: Sets identities

Q: Let X = {a, b, c, d,e} and let T = {X, Ø, {a}, {a,d}, {a,e}}, then * (X, T) is not Hausdorff but it…

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

Q: 2. Let A = {0, 1, а, b, 8, 10, с, — 4}, В %3 {3, 1, 9, e, а, с, 0}, and C 3D {2, с, 10, 9, 8, —4,…

A: solution of the given problem is below...

Q: Let u = (3, 1, 2), 1 = (1,0,1), v2 (2, 1, 3), v3 = (4, 2, 6). Find C₁, C2, C3 such that = u = C1v₁ +…

A: In this question, we want to find the values of the cofficients of the given linear combination of…

Q: O Ho: H Diff = 0; H, H O Ho: H Diff = 0; H, H Diff >0 O Ho: Holder =H Youngeri Hai Holder>HYounger O…

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Q: Let X = {a, b, c, d, e} and let T= {X, Ø, {a), {c,d}, {a,c,d}, {b,c,d,e} }, then O X T) is neither…

A:

Q: Let X = {1,2,3,4} SUCH THAT TX = {4, {2},{1,2},{2,3} , {1, 2, 3},X}: AND Y = {1,3,4} C X, THEN TY =

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

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

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

Q: Determine whether or not the set {(2, 21, 0), (1, 2, 5), (7, 21, 5)} islinearly independent over R.

A:

Q: Let U be the universal set, where: U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} Let sets A, B and C be…

A: Given set U={1,2,3,4,5,6,7,8,9,10} A={1,6,7,10} B={2,3,10} C={1,3,4,5,6}

Q: Set C and the universal set U are defined as follows. U={p,q,r,x,y,z} C={p,q,x}

A: Given,        Set C and the iniversal set U are defined as follows :         U=p,q,r,x,y,z…

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

A:

Q: Let U={a,b,c,d,e,f.g,h,k}, A={a,b,c,g}, B={d,e,f,g}, C={a,c,f} and D={f,h,k} 1. Compute: a.) A U B…

A:

Q: Let U={a,b,c,d,e,f,g,h,k}, A={a,b,c,g}, B={d,e,f.g}, C={a,c,f} and D={f,h,k} 1. Compute: a.) A U B…

A:

Q: Let u = {1, 0, 2}, v = {0, 1, 3} and w {1, 0, 1}, then

A: Let u={1,0,2},v={0,1,3} and w={1,0,1} .

Q: Let U = {q, r, s, t, u, v, w, x, y, z} A = {q, s, u, w, y} B = {q, s, y, z} C = {v, w, x, y, z}. %3D…

A:

Q: The set {u1, u2, u3} is orthonormal. 1 2 V5 V5 1 2 1 2 10 ,U2= ,u3= 10 1 2 1 2 10 10 True False

A:

Q: Let U = {1,4,5,8,9,10,13,15,16}, X = {4,8,10,15}, Y = {4,5,8,9,10}, and Z = {1,4,5,15,16}. List the…

A: Given:     U=1,4,5,8,9,10,13,15,16    X=4,8,10,15    Y=4,5,8,9,10  Z=1,4,5,15,16 Find:…

Q: Let Z = {a, b, c, d}. What is the cardinality of the Power Set of Z, |P(Z)|?

A: Power set:Power set of any set S is the set of all subsets of S, including the empty set and S…

Q: {(x,a), (x,b), (x,c), (y,a), (y,b).(y,c)} is the Cartesian product AXB of two sets given as A =…

A: our objective is to find A

Q: Let A = {c, d, f, g), B = {f, j}, and C = (d, g}. CsA A) True (B) False

A:

Q: Let U- lo, 1,2, 3,4,5,6,7,8,a}.let two fuzzy subsets A and B •f 0 be given by 2 3 4 6 7 8 9 0:2 0:3…

A: We have to find A∨B, A∧B, Ac, and Bc for the given data…

Q: let Z={X/ 5< X <7}, Y={ X/ O < X < 8} , S={X/ Os X s 11} then y n Z = O {8 ,9,10,11} O (9,10,11} O…

A:

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

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

Q: Let X = {a, b, c, d,e} and let T= { X, Ø, {a}, {a,d}, {a,e} }, then * O (X,T) is Hausdorff and…

A:

Q: 2. Let A = {0, 1, а, b, 8, 10, с, — 4}, В 3D {3, 1, 9, e, а, с, 0}, and С %3D {2, с, 10, 9, 8, —4,…

A: Using the definition of intersection, union and difference between two set

Q: Let U = {q, r, s, t, u, v, w, x, y, z} A = (q, s, u, w, y} B = (q, s, y, z} C= (v, w, x, y, z}…

A: Topic:-  set and sub set

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”.