Prove the following using the specified technique:A) Letxandybe two real numbers such thatx yis rational. Prove by contrapositive that ifxis irrational, thenx−yis irrational. B) Prove by contradiction that for any positive two real numbers, xandy, ifx·y≤50, theneitherx <8 ory <8.

Following are the solution to this question:

Explanation:

In point A:

The predicate of the whole argument is if x+y is rational and x-y is reasonable, then x is reasonable as well" To see the sum of the two logical estimates is often sound. Let us be two real .rs amount then seeing how.  

is logical, too. x Thus if is logical and is true, then should be sound.  

Let's assume Therefore the rational proves the necessary statement in the query.  

In point A:

Let , both to demonstrate it through contradiction. So,. This implies that both are valid in the very same period. The argument is valid.