Final answer:
In this interpretation, the truth value of each predicate wff is as follows: a. False, b. True, c. True, d. True.
Step-by-step explanation:
In the interpretation where the domain is all integers, and A(x) is 'x < 5' and B(x) is 'x < 7', let's translate and determine the truth value of each predicate wff.
a. (3x)(Ax): This means 'For every integer x, x is less than 5.' The truth value of this statement is False because there are integers greater than or equal to 5.
b. (3x) [A(x) B(x)]: This means 'For every integer x, if x is less than 5, then x is also less than 7.' The truth value of this statement is True because all integers less than 5 are also less than 7.
c. (vx) [A(x)→ B(x)]: This means 'There exists an integer x, such that if x is less than 5, then x is also less than 7.' The truth value of this statement is True because we can find integers less than 5 that are also less than 7, like 4.
d. (vx)[B(x) → A(x)]: This means 'There exists an integer x, such that if x is less than 7, then x is also less than 5.' The truth value of this statement is True because all integers less than 7 will also be less than 5.