Recall \(\Z = \{\ldots,-2,-1,0, 1,2,\ldots\}\) (the integers). Let \(\Z^+ = \{1, 2, 3, \ldots\}\) be the positive integers. Let \(2\Z\) be the even integers, \(3\Z\) be the multiples of 3, and so on.
Is \(\Z^+ \subseteq 2\Z\text{?}\) Explain.
Is \(2\Z \subseteq \Z^+\text{?}\) Explain.
Find \(2\Z \cap 3\Z\text{.}\) Describe the set in words, and using set notation.
Express \(\{x \in \Z \st \exists y\in \Z (x = 2y \vee x = 3y)\}\) as a union or intersection of two sets already described in this problem.