D= {x|x is a whole number} e = {x|x is a perfect square between 1 and 9} f = {x|x is an even number greater than or equal to 2 and less than 9} d∩f is {4, 6}.
a. true.
b. false.

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

•  D = {x | x is a whole number}

D = ℤ

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

•  E = {x | x is a perfect square between 1 and 9}

("between" does not include the boundaries)

E = {x | x is a perfect square, 1 < x < 9}

E = {x | x = k²,  k ∈ ℕ  and  1 < x < 9}

E = {2²}

E = {4}

•  F = {x | 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. =)

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