Let P(m,n) be the statement "m divides n" where the

QUESTION:

Let \(P(m, n)\) be the statement " \(m\) divides \(n\)," where the domain for both variables consists of all positive integers. (By " \(m\) divides \(n\) " we mean that \(n=k m\) for some integer k.) Determine the truth values of each of these statements.

a) \(P(4,5)\)

b) \(P(2,4)\)

c) \(\forall m \forall n P(m, n)\)

d) \(\exists m \forall n P(m, n)\)

e) \(\exists n \forall m P(m, n)\)

f) \(\forall n P(1, n)\)

Equation Transcription:

Text Transcription:

P(m,n)

m  

n  

n=km  

P(4,5)  

P(2,4)  

Forall m forall nP(m,n)  

Exists m forall nP(m,n)  

Exists n forall mP(m,n)  

forall nP(1,n)