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Question
Are the sets A = {4, 5, 6} and B = {x : x2 – 5x – 6 = 0} disjoint?
Solution
A = {4, 5, 6}
B = {x : x2 - 5x - 6 = 0}
x2 - 5x - 6 = 0
⇒ x2 - 6x + x -6 = 0
⇒ x(x - 6) +1(x - 6) = 0
⇒ (x - 6) (x+1) = 0
∴ Either x - 6 = 0x
⇒ x = 6
Or
x+1 = 0
⇒ x = -1
∴ B = {6, -1}
Hence set A and set B are not disjoint because these sets have element 6 in common.
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