Final answer:
To prove that (∀x)(P(x)∧Q(x)) implies (∀x)P(x)∧(∀x)Q(x), we can utilize the laws of logic and the property of universal distribution.
Step-by-step explanation:
For part b, to prove that (∀x)(P(x)∧Q(x)) logically implies (∀x)P(x)∧(∀x)Q(x), we can use the laws of logic. By universal distribution, we know that if every element in a domain satisfies both P(x) and Q(x), then every element satisfies P(x), and every element satisfies Q(x) separately. In more formal terms, if for every x in the domain, both P(x) and Q(x) are true, then it is implied that for every x, P(x) is true, and for every x, Q(x) is true respectively. This is because the conjunction inside the parentheses applies to each P(x) and Q(x) individually for all x, thereby allowing them to be 'distributed' outside the parentheses as separate universal quantifications.