Answer and Step-by-step explanation: Law of deduction is a mathematical logic that states the following:
1) If p happens, then q happens;
2) p is true;
Then, a there is a third statement that is
3) q is also true.
In this question,
If a polynomial is prime, then it cannot be factored.
Statement p is that 5x + 13y is a polynomial and is prime, i.e., p is true.
Statement q is that "it cannot be factored"
Therefore, 5x + 13y cannot be factored.
The law of detachment is used to confirm or refute a claim.
The true statement is: 5x + 13y cannot be factored
The law of detachment states that; for statements p and q
(1) If p then q
(2) p
If the above statements are true, then the following statement is true
(3) q
The statements in the question can be represented as:
(1) If 5x + 3y is a polynomial and is prime then it cannot be factored
(2) It cannot be factored
Using the above representations of p and q, as an illustration; the third statement would be:
(3) 5x + 3y is a polynomial and is prime
Since the third statement is true, then we can conclude that
5x + 13y cannot be factored
Read more about law of detachment at:
https://brainly.com/question/13966470
