Question

In the following, state whether A = B or not: (i) A = { a , b , c , d }; B = { d , c , b , a } (ii) A = {4, 8, 12, 16}; B = {8, 4, 16, 18} (iii) A = {2, 4, 6, 8, 10}; B = { x : x is positive even integer and x ≤ 10} (iv) A = { x : x is a multiple of 10}; B = {10, 15, 20, 25, 30 ...}

Answer 1

(i)

A={ a,b,c,d }

B={ d,c,b,a }

The condition for both the sets to be equal is that all the elements of a set must be there in the other set. Although the order is not same, but set A has all the elements, i.e., a,b,c,d as that inset B .

Hence, A=B

(ii)

A={ 4,8,12,16 }

B={ 8,4,16,18 }

Set A contains element 12 which is not in set B .

Hence, A≠B

(iii)

A={ 2,4,6,8,10 }

B={ x:x is a positive even integer and x≤10 } ={ 2,4,6,8,10 }

All the elements of set A are there in set B .

Hence, A=B

(iv) A={ x:x is multiple of 10 } ={ 10,20,30,40,50..... }

B={ 10,15,20,25,30.... }

The element 15 belongs to set B , but is not in set A .

Hence, A≠B .