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, c},  find the following. (a)     n(Ac) (b)     n(A ∩ Bc) (c)     n(A ∪ Bc) (d)     n(Ac ∩ Bc)

Q: 4. Let B = {1, 2, 3, 4, 3, 2, 1}. What is |B|?

A: We will solve the following

Q: let u=(1,2,3), v=(3,2,1) and w=(4,5,6) u.(2v)= Select one: 1/20 20 -20 -1/20

A: The given vectors are: u=(1, 2, 3)v=(3, 2, 1)w=(4, 5, 6)

Q: In (IR, Tu), if A = (3,5) n (Q – N) then A %3D

A: Given that in the topological space ℝ, τu ( the usual topological space )            A=3,5∩ℚ-ℕ Then…

Q: . If n(A) = 15, n(B2)= 20, and n(A ∩ B) = 10,find n(A ∪ B)

A: Given: nA=15, nB=20, nA∩B=10

Q: 3. Let A = {1, 2, 3}. What is |A|?

A: If A = {x,y,z}  |A| = sqrt x^2 + y^2 + z^2

Q: Let S = {0, 1, 5, 4, 7}, number of subsets of S is 32Q, then find the value of Q.

A: S is a set with cardinality 5 and given he number of subsets of S is 32Q, then we have to find the…

Q: f P(A) = 0.18, P(B) = 0.35 and P(A ∩ B) = 0.07, find the following: a. P(A ∪ B) b. P(A\B) c. P…

A: Given that  P(A) = 0.18,  ;  P(B) = 0.35  ; P(A ∩ B) = 0.07 ;    We know that By addition theorem…

Q: If a(3, 4) – b(2, 4) = (8, 10), determine a and b.

A:

Q: 2. (i) (1 2 3 4 5) (2 5 4 3 1) and (1 5 3 2 4) Find the product of the permutations: (a, az ... Ax)…

A: NOTE- Since the terms in the last bracket of first part are not clear, so solving just second part…

Q: Let R = {(3,4),(1,3),(4,2),(4,1)}, Then R² is given by O (1,3),(2,1),(3,2),(4,3)} O {(1,3).(2,1).(3,…

A:

Q: Let A = ff, I, y }, B = {r, a, t}. Find A x B and B x A. AxB= BxA= Let A = ff, I, y }, B = {r, a,…

A:

Q: Can you find a,b,c, and d (if exists) such that AB = BA.

A:

Q: 5. Given R ={(1,1), (1, 3), (2, 1), (2,2), (2, 3), (3, 1)} on {1,2,3,4}. Thus, R is reflexive. A.…

A: Given problem :- Given R = {(1,1), (1, 3), (2, 1), (2,2), (2, 3), (3, 1)) on {1,2,3,4). Thus, R is…

Q: Suppose E = {a, b, c, d, e, f, g, h, i, j}, %3D A= {a, b, c, d, e, f, g}, B= {b, d, f, i, j}, C =…

A: Given sets are

Q: Let A, B, C subset U. Suppose that n(U)= 90, n(A)= 40, n(B)= 55, and n(C)= 20. Which of the…

A: Answer

Q: 5. Let A 3D, В %3 and C %3 Find a) (A · B)C b) А : (2С) c) ||B||2

A:

Q: If A+B=X and A-B=Y then...?

A: System of linear equations,

Q: 4. Define = {1,2,3,4,5,6} and A₁ = {i} for i = 1,2, ...,6, B = {1,4}, C = {2,3,4}, D = {1,2,3} and E…

A:

Q: Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. {1,3,4} U {5,7}

A: For two sets A and B, A ∪ B implies the set of elements that belong to set A or B.

Q: Let A = {a, b, c, d}. Find P(A).

A: Let A = {a, b, c, d}. Find P(A).

Q: P(3, -2, -1), Q(1, 5, 4), R(2, 0, -6), S(-4, 1, 5) find proj PS. QR

A:

Q: . If n(A) = 30, n(B) = 40, and n(A ∪ B) = 45,find n(A ∩ B).

A:

Q: 3. Consider A={m,a,t,h}; C={x:x=3n,1sns4,neN}; B={s,t,e,m} ; D={x:x=2n,15n S6,nEN} What is ANB?

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

A:

Q: Let A %3D {1,2,3, 4}, В %3D {3,4, 5},С %3D {а, b, с}. Find A n B, A x С, В х С, (АnВ) х ( (Ах С)n (В…

A:

Q: Let Ai = = [i, i + 1], i = 1, 2, 3, Then A₁ A2 A3 A4 is. a. {1,2,3,4,5} b. (1,5) d. [1,5] ....

A: We have given that Ai=[i,i+1]A1=[1,2]A2=[2,3]A3=[3,4]A4=[4,5]

Q: If n(A) = 62, n(B) = 19, and n(A ∩ B) = 4, find n(A ∪ B).

A:

Q: Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 4}, B = {2, 4, 6, 8} the A' - B' =

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”.