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प्रश्न
State, if the following pair of a set is equal or not:
A = {x : x ∈ N, x < 3} and B = {y : y2 - 3y + 2 = 0}
उत्तर
A = {x : x ∈ N, x < 3}
= {1, 2}
B = {y : y2 - 3y + 2 = 0}
y2 - 3y + 2 = 0
⇒ y2 - 2y - y + 2 = 0
⇒ y(y - 2) -1(y - 2) = 0
⇒ (y - 2)(y - 1) = 0
∴ Either y - 2 = 0
⇒ y = 2
Or
y - 1 = 0
⇒ y = 1
∴ B = {1, 2}
Now we see that elements of sets A and B are the same (identical).
∴ Sets A and B are equal.
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