Q5. If {x, y} = {1, 2}, find all possible x and y.
x = 1, y = 2 or x = 2, y = 1: both elements of {1, 2} must appear, and order does not matter.
Q6. Are {1, 2, 3} and {x : x ∈ N and x < 4} equal? Are {1, 2, 3} and {x : x ∈ Z and x < 4} equal?
The first pair is equal: the natural numbers below 4 are 1, 2 and 3. The second is not: the integers below 4 include 0, −1, −2, …, so that set is infinite.
Q7. If {2, x} = {2, 5}, find x. If {2, x} = {2}, find x.
First case: 5 ∈ {2, 5}, so 5 must be in {2, x}; since 5 ≠ 2, x = 5. Second case: x ∈ {2, x}, so x must be in {2}, giving x = 2; then {2, 2} = {2}, since repetition does not change a set.