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}

Answer 1

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.