The facts that are assumed and the facts that are proven in a direct proof of the theorem is that option a) Assumed: x is rational and y is rational and Proven: x + y is rational.
The term known as theorem is known to be a kind of a formula, or statement that is seen in a lot of mathematics field and it also known top be the logic deduced.
Note that it is also seen as the result that is said to have been proved to be true (through the use of operations and facts that are said to be already known).
Therefore, The facts that are assumed and the facts that are proven in a direct proof of the theorem is that option a) Assumed: x is rational and y is rational and Proven: x + y is rational.
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Theorem: For any two real numbers, x and y, if x and y are both rational then x + y is also rational. Which facts are assumed and which facts are proven in a direct proof of the theorem?
a) Assumed: x is rational and y is rational
Proven: x + y is rational
b) Assumed: x + y is irrational
Proven: x is irrational and y is irrational
c) Assumed: x + y is rational
Proven: x is rational or y is rational
d) Assumed: x is rational or y is rational
Proven: x + y is rational
