Q5 of 23 Page 38

If A = {x : x is a natural number}, B = {x : x is an even natural number} C = {x : x is an odd natural number} and D = {x : x is a prime number} Find A B, A C, A D, B C, B D, C D.

A = {1, 2, 3, 4, 5 …}


B = {2, 4, 6, 8 …}


C = {1, 3, 5, 7 …}


D = {3, 5, 7, 11 …}


We know that the intersection of sets A and B is the set of all elements which are common to A and B.


A ⋂ B = {1, 2, 3, 4, 5 …} ⋂ {2, 4, 6, 8 …} = {2, 4, 6 …} = Even natural number


A ⋂ C = {1, 2, 3, 4, 5 …} ⋂ {1, 3, 5, 7 …} = {1, 3, 5 …} = Odd natural number


A ⋂ D = {1, 2, 3, 4, 5 …} ⋂ {3, 5, 7, 11 …} = {3, 5, 7 …} = Prime number


B ⋂ C = {2, 4, 6, 8 …} ⋂ {1, 3, 5, 7 …} = ϕ


B ⋂ D = {2, 4, 6, 8 …} ⋂ {3, 5, 7, 11 …} = ϕ


C ⋂ D = {1, 3, 5, 7 …} ⋂ {3, 5, 7, 11 …} = {3, 5, 7 …} = Prime number


More from this chapter

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3

If A = {2, 4, 6, 8, 10} and B = {3, 6, 9, 12, 15}, find A – B and B – A.

 4

If A and B are two sets such that then what is

6

If A = {3, 6, 9, 12, 15, 18, 21}; B = {4, 8, 12, 16, 20} C = {2, 4, 6,8, 10, 12, 14, 16}; D = {5, 10, 15, 20} find

(i) A – B (ii) A – C


(iii) A – D (iv) B – A


(v) C – A (vi) D – A


(vii) B – C (viii) B – D


(ix) C – B (x) D – B

 7

State whether each of the following statement is true or false. Justify you answers.

(i) {2, 3, 4, 5} and {3, 6} are disjoint sets.


(ii) {a, e, i, o, u} and {a, b, c, d} are disjoint sets.


(iii) {2, 6, 10, 14} and {3, 7, 11, 15} are disjoint sets.


(iv) {2, 6, 10} and {3, 7, 11} are disjoint sets.