Question

Is Z is a positive number a statement in logic? why​

Answer 1

Answer:

There are two issues here. One is that the logic statement you offer does not match the English statement. The logic statement you offer (when you add ∀y as Mauro Allegranza suggested in the comments) would be best translated to English as: The sum of any two positive numbers is (necessarily) positive.

For the English statement "The difference of two positive numbers is not necessarily positive", you would want something like:

¬∀x∀y(x>0∧y>0→x−y>0)

or, equivalently,

∃x,y such that (x>0∧y>0∧x−y<0)

The second issue is the question you raise about how "necessarily" figures in these statements. "Necessity" is a phrase used in many ways, often unclearly. For your purposes, in your original English sentences, "necessarily" almost certainly means simply that some positive numbers have negative difference.

Step-by-step explanation:

PL follow m