which relationships are true?

Question

Which relationships are true? Hint: the List of symbols in the front cover will help)
a)Q ⊆ Z
b)Q ∪ Z = Q
c)Z^+ U Q =Z

Answer 1

Q is the rational numbers - defined as any number that can be described as a ratio of integers. It includes the integers (Z) because every integer m can be described as m/1. But Q includes numbers like 1/2 or 1/3 that are not integers. So clearly a is not true, as to have A a subset of B, every element of A must be an element of B. b is true, since taking the union of Q and Z is the rationals and the integers, which is by the previous the rationals. c is false by the same discussion as above - if you take the union of a set with the rationals you do not end up with a subset of the integers because there will be numbers like 3/4 in the set.