I am struggling with the following question, first time dealing with sets that state that the elements within are greater/less than and equal to an integer.
Let $R$, $S$ and $T$ be sets defined as follows.
$R = \{x : x \in \mathbb{Z} \text{ and either } x \leq −2 \text{ or } x \geq 5\}$
$S = \{−3, −2, 4, 5, 6\}$
$T = \{x : x \in \mathbb{Z} \text{ and } x \geq 2\}$
Find $R - T$
Can I say that $R - T = \{x : x \in \mathbb{Z} \text{ and } x ≤ −4 \text{ or } x ≥ 7\}$
Find $(R\cup S) - (R\cap S)$
Can I say that this is equal to $\{x : x \in \mathbb{Z} \text{ and } x \leq −4 ,\, 4, \text{ and } x \geq 7\}$
I get the feeling that I am way off. I generally draw a venn diagram to get a better understanding of what the question is asking, but in this can I can't :( Please lend a helping hand.
In the case of $R\setminus T$ we have
$$R\setminus T = \{x : x \in \mathbb{Z} \text{ and } x \leq -2\}$$
Because it's the same as $R$ minus all those $x \in \mathbb{Z}$ such that $x\geq 2$ (which includes $x \geq 5$)
For $(R\cup S) - (R\cap S)$ what you wrote is OK.