Question

Which diagram represents the following sets?



P = {x | x is an integer divisible by 2}; Q = {x | x is an odd integer}; R = {x | x is an integer divisible by 3}



Circle P overlaps with circle R. Circle R also overlaps with circle Q.

Circles P, Q, and R overlap each other.

Circles P and R overlap. Circle Q is beside the 2 circles.

Answer 1

Choose the first diagram: "Circle P overlaps with circle R. Circle R also overlaps with circle Q."

Reason: P (even integers) and Q (odd integers) are disjoint, so P and Q must not overlap. P ∩ R is nonempty (multiples of 6, e.g. 6) and Q ∩ R is nonempty (odd multiples of 3, e.g. 3), but P ∩ Q ∩ R is empty (no integer can be both even and odd). The first diagram matches those intersections.