Operations on Sets

Exercise

  1. Let A = {-5, -3, 0, 3, 5}, B = { -4, -2, 0, 2, 4} and
    = { -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5}
    (i) Find AB
    (ii) Find AB
    (iii) Verify that n(AB) = n(A) +n(B) -n(AB)
    (iv) Find A'
    (v) Verify that n(A) +n(A') = n()
    (vi) Find B'
    (vii) Verify that n(B) +n(B') = n()
    (viii) Find AA' and AA'
    (ix) Find BB' and BB'
    (x) Find (AB)' and A'B'. Verify that they are equal.
    (xi) Find (AB)' and A'B'. Verify that they are equal.
    (xii) Find A -B and B -A. Are they equal?
  2. Let A = {x | x is an even natural number less than 20} and
    B = {x| x is a multiple of 3 less than 20}
    Represent A and B by Venn diagrams. Hence find AB and AB.
  3. Let A = {students who like cricket} and B = {students who like tennis}.
    Let n(A) = 20, n(B) = 15 and n(AB) = 5. Find n(AB).
  4. Let n() = 50, n(A) = 15, n(B) = 13, n(AB) = 10.
    Find n(A'), n(B'), n(AB).
  5. In a city, 50% people read newspaper A, 45% read newspaper B and 25% read neither A nor B. How many individuals read both the newspapers A as well as B?
  6. Let = {triangles}, I = {isosceles triangles}, E = {equilateral triangles},
    R = {right angled triangles} and P = {obtuse angled triangles}.
    (i) Draw a Venn diagram to show these sets in their correct relationship.
    (ii) Shade the region representing IR and write the measures of the angles of the triangles of this region.
  7. The students of a certain school have a choice of three games: Tennis, Badminton and Cricket. The following table gives the percentage of students who play some or all the games:
    Games Tennis Badminton Tennis and Badminton Badminton and Cricket Cricket and Tennis Cricket only All Games
    % of students 35 30 10 10 8 30 3
    Draw a Venn diagram and use it to determine the percentage of students who
    (i) play Tennis only
    (ii) play Badminton only
    (iii) play Cricket
    (iv) do not play any of the games.

Answers

 1.(i) {-5, -4, -3, -2, 0, 2, 3, 4, 5}     (ii) {0}
    (iv) {-4, -2, -1, 1, 2, 4}                 (vi) {-5, -3, -1, 1, 3, 5}
    (viii) AA' = , A A' =              (ix) BB' = , BB' =
    (x) {-1, 1}                                      (x) {-5, -4, -3, -2, -1, 1, 2, 3, 4, 5}
    (xii) A -B = {-5, -3, 3, 5} and B -A = {-4, -2, 2, 4}. They are not equal.
2. A = {2, 4, 6, 8, 10, 12, 14, 16, 18} and B = {3, 6, 9, 12, 15, 18}.

                 
       AB = {2, 4, 6, 8, 10,12, 14, 16, 18, 3, 9, 15}    AB = {6, 12, 18}
3.
     nbsp;nbsp;  
        n(AB) = 15 +5 +10 = 30
4. n(A') = 35, n(B') = 37, n(AB) = 18
5. 20%
6. (i)
      
     (ii) 45°, 45°, 90°
7. (i) 20%        (ii) 13%           (iii) 45%             (iv) 15%.