Let E CR and F C R. Let X = {(r,y)|:r,yE IR and y = I}. Prove that ifX C E X F, then E x F = R2 by ling out gaps in the following argument. Proof. We are given that X C _. We need to show that _ and Let (11,5) E E X F. Then, a E_ and b E_. If a. E_, then a E_ because E C_. If I; E_T then b E_ because F C_. Therefore, (o,b) E 13.2 because _. We showed that _. Let ((1,5) E 1R2. Then, a E_ and b E_. Therefore, by denition of X , we have (and) E K and (b,b) E X. Since (the) E X and _, we have _. Since (b,b) E X and we have _. Therefore, (a, b) E E X F. We showed that _. _T