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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.
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jjkool13
Answer:
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.
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