Can I get number 414 answered please Let q be a positive int

Can I get number 4.14 answered please.

Let q be a positive integer for which q (1/m - 1/m) > 1. Then let p be any integer for which q/n

4.14: Proof dose not guarantee about \"p not equal to zero\".

4.13:

Ans a) rational number should be in the form p/q where q not equal to zero.

Ans b) Yes, since m and n are positive numbers such that m<n, there exist positive number such that (1/m-1/n)>1/q.

Ans c) Yes, Since (1/m-1/n)>1/q implies (q/m-q/n)>p/q implies1/n<p/q<1/m.

Ans d) Yes, Since q/n<p<q/m implies 1/n<p/q<1/m because r=p/q.

Ans e) in q(1/m-1/n)>1