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 show that ( A ∪ B )′ = A′∩ B′.

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: Given that U = {1,2, 3, ..., 11, 12, 13} A = {1, 2, 7, 12} В 3 3,5, 6, 8, 12, 13} С 3 {1,5, 7, 8,…

A: Explanation: Region I:   2 Region II:  Null Region III:  3,6 Region IV:  1,7 Region V:  12 Region…

Q: Let V = { a, e, i, o, u } andB = { a, i, k, u}. Find V – B and B – V

A: V-B= elements those lie in V but not in B  Hence, V-B={e,o}

Q: Consider the sets A={a, e, i, o, u} and B={c, m, n, r, s, v, w, x, z}. Which of the following is not…

A: Consider the sets A={a, e, i, o, u} and B={c, m, n, r, s, v, w, x, z}. Which of the following is not…

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

A: To determine the elements of the set given below

Q: Let U=​{q,r,s,t,u,v,w,x,y,z}, A=​{q,s,u,w,y}, and B=​{q,s,y,z}. List the elements in the set (A ∩…

A: we know that , X ' = U - X

Q: Let U = {−4, −3, −2, 0}, V = {a, b, c}. How many subsets does the set U × V have?

A:

Q: Let X={a,b,c,d), f = ((a,b),(b,a),(c,c),(d,d)}CX×X, and g= ((a,d),(b,a),(c,b),(d,c)}CX×X. Find gof.…

A: Use the definition of composition of functions to solve this problem as in next step.

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 A=span(u,v) and B=span(u,v,w). Which statement is true? - A ≠ B and that is all you can say…

A: Let A=span(u,v) and B=span(u,v,w).

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

A:

Q: Let U, A, B, and C be defined as shown below. U= [ a, b, c, d, e, f, g, h, i, j } A = { d, e, g, h,…

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 A, = {..., – 2, – 1,0,1,..., i}. Find ỦA, i31

A: First we find A1, A2, A3,...An, then find union as in next step.

Q: Let a1, a2 and a3 be colums of A, i.e A = [a1,a2,a3] and let W = span {a1,a2} compute projw a3.

A:

Q: 48. Let A, = {...,-2, –1,0, 1, ...,i). Find %3D a) Aj. b)4-

A: The meaning of the set  ∪i=1n Si where S1,S2,……,Sn are the sets . The set ∪i=1n Si is collection of…

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= (q, r, s, t, u, v, w, x, y, z); A= {q, s, u, w, y}; B={q, s, y, z} and C= {v, w, x, y, z).…

A: 1)Given that  U={q, r, s, t, u, v, w, x, y, z}; A= {q, s, u, w, y},  B = {q, s,  y, z} and  C = {v,…

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: If R is a UFD and f(x) , g(x) are elements of R[x] , then c(fg) = c(f)c(g), do not copy paste…

A:

Q: If S is a subset of T , then u* (T) sµ* (S). ylgn O İhi O

A: False

Q: Let A, and Az be two subsets of R. Show that m. (A, x A2) S m*(A,) m*(A2).

A: To prove: m*(A1 * A2) ≤ m*(A1) m*(A2)

Q: Let A = { a, e, i, o, u } and B = { a, i, u }. Show that A ∪ B = A

A: A ∪ B ={ a, e, i, o, u } ∪ { a, i, u }           = { a, e, i, o, u }          = A

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

A: Consider the given sets, U=a,b,c,d,e,f,g,h,i,j,kA=a,b,f,h,i,jB=a,c,d,h,jC=a,d,f,g,j We need to…

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

A: Option 1 is correct.

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

A:

Q: Let U= {1,2,3,4,5,6,7,8,9,10,11} A= {3,5,8,11} B= {2,5,6,7,8} C= {3,4,6,7,8,10,11} D= {1,3,5,6}…

A:

Q: If S is a subset of T , then u* (T) sµ* (S) ylgn C ihi O

A: I will use the definition of measure to answer the question.

Q: find the complement of set B, given that U= {x ∈ z/ - 7 < x < 7}     A= {x ∈ z+ /2 < x < 6}     B=…

A:

Q: Let U = {m,a,t,h,e,w,d,i,n}   X = { e,w,m,a,t}              y = {e,w,d,i,n}            Z= {h,e,w}…

A: U = {m, a, t, h, e, w, d, i, n}   U= Universal set X = {e, w, m, a, t}              Y = {e, w, d, i,…

Q: Let U = R, A =[-6, 3), B = (-1,5), and D = [-7, 1]. Find (i) AN Bº (ii) (BUD)e

A: We use De' Morgan's law and union, intersection and complement of set to answer the given question.

Q: Let U%3D {а, с, е, h, m, о, р, s, t, и, у, 0, 1, -} А %3D {с, һ, о, р, s, и, e, y} B = {s, e, t} С…

A: The power set of a set S denoted by 2S is defined as the set of all subsets of the Set S including…

Q: Let w = (2, − 1, 1), v = (− 4, − 5, 1), and u = (6, − 2, 2). Find u × (v × w)

A:

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: 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,yz}. List the elements in the set.A'uB

A: Given , 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,…

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

A: Given Information -  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} We have…

Q: Let U= {1,2,3,4,5,6,7,8,9,10,11} A= {3,5,8,11} B= {2,5,6,7,8} C= {1,3,5,6} D= {3,4,6,7,8,10,11}…

A: Given sets are U= {1,2,3,4,5,6,7,8,9,10,11} A= {3,5,8,11} B= {2,5,6,7,8} C= {1,3,5,6} D=…

Q: How to solve this?

A:

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

A:

Q: Given U = {a,b,c,d,e,f,g,h,ij}, A = {b,d,f,hj} B = {e,f,g,h,ij} find the following sets. a.…

A: Here, the given sets are: U=1,b,c,d,e,f,g,h,i,jA={b,d,f,h,j}B={e,f,g,h,i,j}

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: 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”.