Originally Posted by

**zhupolongjoe** 1) Give the grade of A(correct), C(part correct), F(incorrect because claim is wrong or proof is wrong)

Claim: The relation T on RxR given by (x,y)T(r,s) iff x+y=r+s is symmetric.

Proof: Suppose (x,y) belongs to RxR. Then (x,y)T(y,x) because x+y=y+x. Therefore, T is symmetric.

What is the grade and why?

I say it is A since the proof generally seems correct and it makes logical sense.

2) Give the proof grade A (correct), C(part correct), F(wrong because claim or proof wrong)

Claim: the relation W on RxR given by (x,y)R(r,s) iff x-r=y-s is symmetric.

Proof: Suppose (x,y) and (r,s) are in RxR and (x,y)W(r,s). Then x-r=y-s. Therefore, r-x=s-y, so (r,s)W(x,y). Thus W is symmetric.

What is the grade and why?

I say it is F since x-r is not the same as r-x, so the claim itself is wrong...i.e proof of something false.