Question

Theorem: If x and y are positive real numbers then xy≥x or xy≥y . A proof by confradiction of the theorem start by assuming which fact? a. There exists two real numbers, x and y, such that xy

Answer 1

To prove the theorem by contradiction, we assume the opposite of the theorem, which is that there exist two positive real numbers such that xy is less than x and xy is less than y. This assumption contradicts the theorem, so the theorem is proven to be true.

Step-by-step explanation:

The theorem states that if x and y are positive real numbers, then either xy is greater than or equal to x, or xy is greater than or equal to y. To prove this theorem by contradiction, we start by assuming the opposite of the theorem, which is the negation of either of the two options.

So, we assume that there exist two positive real numbers, x and y, such that xy is less than x and xy is less than y. This assumption contradicts the given theorem, as it states that xy is greater than or equal to x or xy is greater than or equal to y for any positive real numbers x and y. Since our assumption leads to a contradiction, we can conclude that the theorem is true.