1. Huyang wrote the following proof that the sum of a rational and an irrational must be irrational. Identify the mistake they made in their proof, if they made one. "I will start with a rational number a and an irrational number b and their sum c . I am going to start with the assumption that c is rational. This gives me a+b=c . I will then subtract a from each side to get b=c−a . I know that c−a musts be rational because both ' c and c are rational and the rational numbers are closed under subtraction. So now I have an equation with b as an irrational number equal to c−a a rational number. This is a contradiction and so my assumption that 'c' is rational is incorrect and 'c' must be irrational."
A. Huyang is incorrect because the rational numbers are not actually closed under subtraction.
B. Huyang is incorrect because there are numbers that are both rational and irrational so having a rational number equal to an irrational one is not necessarily a contradiction.
C. Huyang is incorrect because they used a proof by contradiction which is not a valid form of proof.
D. Huyang is correct.