(a) Predicate: 10d is an integer
The domain is [tex]\mathbb{Z}[/tex]. In fact, integers are closed under multiplication, and 10 is an integer. So, if d is an integer, 10d is a multiplication between integers, and thus an integer.
(c) [tex]1\leq x^2\leq 4[/tex]
Since 1 and 4 are both squares, we have
[tex]1\leq x^2 \leq 4 \iff 1^2\leq x^2 \leq 2^2[/tex]
And we deduce that x must be between 1 and 2. But since negative numbers become positive when squared, the numbers between -2 and -1 are also fine. So, the domain is
[tex][-2,-1]\cup [1,2][/tex]
Predicates (b) and (d) are identical to (a) and (c)
