Q5. Show that {x : x ∈ N and x2 − 3x + 2 < 0} is empty.
(x − 1)(x − 2) < 0 means 1 < x < 2, and no natural number lies strictly between 1 and 2.
Q6. Is the set of natural numbers x with x + 5 = 3 empty?
Yes: x = −2, which is not a natural number.
Q7. Give an example of an empty set of your own, described in set-builder form.
For example {x : x is a natural number and x < 1}, or {x : x is a month with 32 days}. Any property that nothing has will do.