Relations and Functions

Relations and Functions

Question

Are the following pair of sets equal? Give reasons :

(i) A = {2, 3}, B = {x : x is solution of x2 + 5x + 6 = 0}

(ii) A = {x : x is a letter in the word FOLLOW}, B = {y : y is a letter of word WOLF}

 

Answer

(i)                   A    =  {2, 3}
                      B   =  { x :  is solution of x2 + 5x + 6 = 0}
 
Now,               x2 + 5x + 6 = 0                   rightwards double arrow      (x+2)(x+3) = 0
 
rightwards double arrow                 x = -2, x = -3            rightwards double arrow     B = {-2, -3}
Clearly,  space space space space space space space space space space space straight A space not equal to space straight B 

(ii)           A = { x: x is a letter in the word FOLLOW
 
rightwards double arrow          A = { F, O, L, W}
Also,       B = { y : y  is a letter of the word WOLF}
rightwards double arrow          B  = { W, O, L, F}
Hence,     A = B.

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