Q13 of 71 Page 23

Use the Venn diagram to answer the following questions


i. List the elements of


U, E, F, E ∪ F and E ∩ F


ii. Find n(U), n(E ∪ F) and n(E ∩ F)

i. From the Venn diagram we get,


U = {1, 2, 3, 4, 7, 9, 10, 11}


E = {1, 2, 4, 7}


F = {4, 7, 9, 11}


∴ E ∪ F = {1, 2, 4, 7, 9, 11} [elements present either in E or in F]


∴ E ∩ F = {4, 7} [elements that are present in both E and F]


ii. U = {1, 2, 3, 4, 7, 9, 10, 11}


∴ n(U) = 8 [no. of elements in U]


E ∪ F = {1, 2, 4, 7, 9, 11}


∴ n(E ∪ F) = 6 [no. of elements in E ∪ F]


E ∩ F = {4, 7}


∴ n(E ∩ F) = 2 [no. of elements in E ∩ F]


More from this chapter

All 71 →
11

Let U = {x : x is a positive integer less than 50}, A = {x : x is divisible by 4} and B = {x : x leaves a remainder 2 when divided by 14}.

i. List the elements of U, A and B


ii. Find A ∪ B, A ∩ B, n(A ∪ B), n(A ∩ B)

 12

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, }, Q = {x : x < 5, }


iii. A = {−3, −2, 0, 2, 3, 5}, B = {−4, −3, −1, 0, 2, 3}

 14

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)’

 1

Place the elements of the following sets in the proper location on the given Venn diagram.


U = {5, 6, 7, 8, 9, 10, 11, 12, 13}


M = {5, 8, 10, 11},


N = {5, 6, 7, 9, 10}