Question

Using appropriate syntax express the following using predicate logic: a) Consumption of food with heavy cholesterol leads to heart diseases, b) Lack of physical activity can lead to type 2 diabetes.

Answer 1

(a) Consider the statement:

where , and

But then "consumption of" is a function which is not in the axiomatic structure of predicate logic and hence cannot be converted into such a statement. Thus the only option we have is to throw that inside a predicate. Thus we have:

where and .

(b) Assuming that "can lead" means "always leads" (because if not, then this is not a mathematical statement as it can have truth values of 0 and 1 both in different situations which is not allowed in predicate logic due to the axiom of excluded middle and the inherent nature of binary predicates). Then, we have:

where and