1.

Which of the following are pairs of equal sets? J = {2, 3} and K = {x : x ϵ Z, (x2 + 5x + 6) = 0}

Answer»

Equal Sets = Two sets A and B are said to be equal if they have exactly the same elements & we write A = B

We have, 

J = {2, 3} 

and K = {x : x ϵ Z, (x2 + 5x + 6) = 0} 

Here, x ∈ Z and x2 + 5x + 6 = 0 

The given equation can be solved as: 

x2 + 5x + 6 = 0 

⇒ x2 + 2x + 3x + 6 = 0 

⇒ x(x + 2) + 3(x + 2) = 0 

⇒ (x + 2)(x + 3) = 0 

⇒ x = -2 and -3 

∴ K = {-2, -3} 

∴ J ≠ K because elements of both the sets are not equal.



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