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Question
Decide which of the following are equal sets and which are not. Justify your answer.
A = {x | 3x − 1 = 2}
B = {x | x is a natural number but x is neither prime nor composite}
C = {x | x ∈ N, x < 2}
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Solution
Since, A = {x | 3x − 1 = 2} ...(Rule method)
3x − 1 = 2
3x = 3
∴ x = 1
x = {1} ...(Roster Method)
B = {x | x is a natural number but x is neither prime nor composite} ...(Rule method)
B = {1} ...(Listing method)
C = {x | x ∈ N, x < 2} ...(Rule method)
N = {1, 2, 3, 4, .....}
C = {1} ...(Listing method)
From (i), (ii) and (iii)
So, A = B = C
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