Prove by contradiction.“The difference of any rational number and an

1.	Prove by contradiction.“The difference of any rational number and any irrational number is irrational”.
Answer» The difference of any rational number and any IRRATIONAL number is irrational. x = a/b for some INTEGERS a and b with b ≠ 0. ... This contradicts the SUPPOSITION that y is rational. [Hence, the supposition is FALSE and the theorem is true.]

Prove by contradiction.“The difference of any rational number and any irrational number is irrational”.

Answer»

The difference of any rational number and any IRRATIONAL number is irrational. x = a/b for some INTEGERS a and b with b ≠ 0. ... This contradicts the SUPPOSITION that y is rational. [Hence, the supposition is FALSE and the theorem is true.]

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Prove by contradiction.“The difference of any rational number and any irrational number is irrational”.​

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Prove by contradiction.“The difference of any rational number and any irrational number is irrational”.