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.