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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} - Mathematics

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Sum

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} 

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Solution

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.

Concept: Types of Sets
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APPEARS IN

Selina Concise Mathematics Class 8 ICSE
Chapter 6 Sets
Exercise 6 (B) | Q 8.4 | Page 67
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