To find the truth set of the predicate P(x): x² < 3, we proceed as follows:
Step 1: The question makes it clear that the domain for the values of x is the set of integers.
Step 2: The predicate P(x) is given by the function x² < 3. This means we are looking for all integer values of x such that, when squared, the result is less than 3.
Step 3: The smallest integer squared that is less than 3 is 0 (since 0^2 = 0), and the largest is 1 (since 1^2 = 1). In between -1 and 1, including them, we find additional values that also satisfy the condition that x² < 3.
Step 4: But keep in mind, that we're looking for integer values, negative integers would also be included. We know that (-1)^2 = 1 and 1 < 3. Thus -1 is also a valid number in the solution.
Step 5: By going through the integer numbers systematically, we find that -1, 0, and 1 are the only integer values which satisfy the given predicate.
So, the truth set for the predicate P(x): x² < 3, when x belongs to the set of integers, is [-1, 0, 1].
Answer: The truth set for the predicate P(x): x² < 3, when x belongs to the set of integers, is [-1, 0, 1].