Q12 of 71 Page 23

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}

i. X = {a, d, f, g, h}


Y = {b, e, g, h, k}


∴ XΔY = {a, b, d, e, f, k} [elements that are present either only in X or only in Y]


ii. P = {x : 3 < x < 9, x ∈}


P contains all the natural number between 3 and 9.


∴ P = {4, 5, 6, 7, 8}


Q = {x : x < 5, x ∈}


The possible values of Q are : 0, 1, 2, 3, 4


∴ Q = {0, 1, 2, 3, 4}


∴ PΔQ = {0, 1, 2, 3, 5, 6, 7, 8} [elements that are present either only in P or only in Q]


iii. A = {−3, −2, 0, 2, 3, 5}


B = {−4, −3, −1, 0, 2, 3}


∴ XΔY = {-4, -2, -1, 5} [elements that are present either only in A or only in B]


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10

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


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v. n(A – C)

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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


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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)

 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)’