Q10 of 71 Page 23

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)

i. A = {3, 6, 9, 12, 15, 18}


B = {4, 8, 12, 16, 20}


∴ A – B = {3, 6, 9, 15, 18} [elements that are present in A but not in B]


ii. B = {4, 8, 12, 16, 20}


C = {2, 4, 6, 8, 10, 12}


∴ B – C = {16, 20} [elements that are present in B but not in C]


iii. C = {2, 4, 6, 8, 10, 12}


D = {5, 10, 15, 20, 25}


∴ C – D = {2, 4, 6, 8, 12} [elements that are present in C but not in D]


iv. D = {5, 10, 15, 20, 25}


A = {3, 6, 9, 12, 15, 18}


∴ D – A = {5, 10, 20, 25} [elements that are present in D but not in A]


v. A = {3, 6, 9, 12, 15, 18}


C = {2, 4, 6, 8, 10, 12}


∴ A – C = {3, 9, 15, 18} [elements that are present in A but not in C]


∴ n(A – C) = 4 [no. of elements in (A – C)]


More from this chapter

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8

If U = , A = {1, 3, 5, 7, 9} and B = {2, 3, 5, 9, 10},

Find


i. A’


ii. B’


iii. A’ ∪ B’


iv. A’ ∩ B’

 9

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)

 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}