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Question
State, if the following pair of a set is equivalent or not:
A = {x : x ∈ N and 11 ≥ 2x – 1} and B = {y : y ∈ W and 3 ≤ y ≤ 9}
Solution
A = {x : x ∈ N and 11 ≥ 2x -1}
11 ≥ 2x -1
⇒ 11 + 1 ≥ 2x -1+1
⇒ 12 ≥ 2x
⇒ `(12)/(2)` ≥ x
⇒ 6 ≥ x
∴ A = {1, 2, 3, 4, 5, 6}
∴ n(A) = 6
B = {y : y ∈ W and 3 ≤ y ≤ 9}
∵ 3 ≤ y ≤ 9
B = {3,4,5,6,7,8,9}
n (B) = 7
Cardinal number of set A = 6 and cardinal number of set B = 7
Set A and set B are not equivalent.
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