Question

Are the following pair of sets equal? Give reasons. (i) A = {2, 3}; B = { x : x is solution of x 2 + 5 x + 6 = 0} (ii) A = { x : x is a letter in the word FOLLOW}; B = { y : y is a letter in the word WOLF}

Answer 1

(i)

A={ 2,3 }

The given equation in set B is defined as,

x 2 +5x+6=0

Solving this for x,

x 2 +3x+2x+6=0 x( x+3 )+2( x+3 )=0 ( x+2 )( x+3 )=0 x=−2 or x=−3

Therefore, B={ x:x is a solution of  x 2 +5x+6=0 } ={ −2,−3 }

The elements in set A are not in set B .

Hence, A≠B .

(ii)

A={ x:x is a letter in the word FOLLOW }

Unique letters in the word FOLLOW are F, O, L, W. Therefore,

A={ F,O,L,W }

B={ y:y is a letter in the word WOLF }

Unique letters in the word WOLF are W, O, L, F. Therefore, B={ W,O,L,F }

Thus, the elements in both the sets are same.

Hence, A=B .