The truth set for each predicate are:
a) d ∈ { -6, -3, -2, -1, 1, 2, 3, 6}
b) d ∈ { 1, 2, 3, 6}
c) x ∈ { [-2, -1] U [1, 2]}
d) x ∈ {-2, -1, 1, 2}
<h3>
How to find the truth set of each predicate?</h3>
We only need to find the sets of values such that the statements are true.
a)
We want to find vales of d, such that d is an integer, and 6/d is an integer.
Here the possible values of d will be:
d ∈ { -6, -3, -2, -1, 1, 2, 3, 6}
Which are all the factors of 6, so all these integers divide 6.
b) Same as before, but this time the domain is a positive integer, so now the truth set will be:
d ∈ { 1, 2, 3, 6}
c) We want to find real values of x such that:
1 ≤ x² ≤ 4
If we apply the square root to the 3 sides, we get two inequalities:
-√1 ≥ x ≥ -√4
√1 ≤ x ≤ √4
Simplifying:
-1 ≥ x ≥ -2
1 ≤ x ≤ 2
So the truth set is:
x ∈ { [-2, -1] U [1, 2]}
c) Same as before, but now we only have integer solutions, so the truth set is:
x ∈ {-2, -1, 1, 2}
If you want to learn more about predicates:
brainly.com/question/18152046
#SPJ1
