## Problems on set-V

In this page 'Problems on set-V' we are going to see problems on complement of set and difference of sets.

Parents and teachers can guide the students to do the problems on their own. If they are having any doubt they can verify the solutions.

The following problems are under complement of a set.

1. (i) If U = {x: 0 ≤ x ≤ 10, x ∈ W} and A = {x: x is a multiple of 3}. Find A'.

(ii) If U is the set of all natural numbers and A' is the set of all composite numbers, then what is A?

2.       If  U =   {a, b, c, d, e, f, g,h},  A= {a, b, c, d} and B = { b, d, f, g}, find

(i) AB      (ii) (A∪B)'       (iii)  A∩B         (iv) (A∩B)'

3.    If    U  =    { x: 1≤ x ≤ 10, xℕ},  A = {1,3, 5, 7, 9} and B = {2, 3,5, 9, 10},

find (i) A'     (ii) B'       (iii) A'∪B'      (iv) A'∩B'

The following problems are under difference of sets.

4.   Given that U= {3,7,9,11,15,17,18}, M = { 3,7, 9, 11} and

N = { 7, 11, 15, 17},

find (i) M-N     (ii) N-M       (iii) N'-M     (iv)  M'-N

(v) M∩(M-N)       (vi)   N∪(N-M)    (vii)n(M-N)

5.    If  A= {3, 6, 9, 12, 15, 18},  B = {4, 8, 12, 16, 20},

C = {2, 4, 6, 8, 10, 12}  and D = {5, 10, 15, 20, 25},

find  (i) A-B      (ii)  B-C    (iii) C-D      (iv) D-A

(v)  n(A-C)       (vi)   n(B-A)

6.    Let  U = {x: x is a positive integer less than 50},

A = {x: x is divisible by 4} and

B = {x: x leaves remainder 2 when divided by 14},

(i) List the elements of U, A and B

(ii) Find A∪B, A∩B, (A∪B)', n( A∩B), A-B and B-A

7.   Find the symmetric difference between the following sets.

(i)  X = {a, d, f, g,h},          Y = {b, e, g, h, k}

(ii)   P = {x: 3<x <9, xℕ},  Q = { x: x<5, x∈W}

(iii)  A = {-3, -2,0, 2, 3, 5},   B = {-4,-3,-1, 0, 2, 3}

8.    Use the Venn diagram, to answer the following questions.

(i) List the elements of  E, F, E∪F and E∩F

(ii) Find n(U), n(E∪F ) and n(E∩F)

9.    use the Venn diagram to answer the following questions.

(i) List U, G and H

(ii) Find G', H', G'∩H', n(G∪H)' and n(G∩H)'

Solutions

Students can try to solve the problems in this page 'Problems on set-V' on their own. Parents and teachers can encourage the students to do so. They can verify their answers with solutions given in this page. If you are having any doubt you can contact us through mail, we will help you to clear your doubt.