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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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