Question

D = x is a whole number E = x F = x D∩F is {4, 6}.

a. true.
b. false.

Answer 1

First, you have to represent each given set by listing their elements. Observe:


• D = x is a whole number

D = ℤ

D = {..., – 3, – 2, – 1, 0, 1, 2, 3, ...}


• E = x

("between" does not include the boundaries)

E = x

E = x = k², k ∈ ℕ and 1 < x < 9

E = {2²}

E = {4}


• F = x is an even number, 2 ≤ x < 9

F = {2, 4, 6, 8}


So,

D ∩ F

= {..., – 3, – 2, – 1, 0, 1, 2, 3, ...} ∩ {2, 4, 6, 8}

= {2, 4, 6, 8} ≠ {4, 6}


Therefore, that statement is false.


I hope this helps. =)