I'm not sure about this one:
prove or give a counterexample to the statement:
if x and y are irrational then x^y is irrational.

Therefore if the gcd of gcd(m,n,i,j)=1 then we can conclude that the number is rational.

Step-by-step explanation:

Negation of the statement: x+y are rational then x and y are also rational

∃m,n,i,j∈Z gcd(m,n)=1 gcd(i,j)=1

Then x=m/n and y=i/j

So when, x+y=mn+ij=m∗j+i∗nn∗j

Therefore if the gcd of gcd(m,n,i,j)=1 then we can conclude that the number is rational.

f is the midpoint of