W 3. Lat R.S.T by rings and let w 4₁ iRDS and I₂ S&T boring. homomorphisms. Show that! V bu b) karty,) c kor (4₂0p), but ker(4₁) / kor (4/₂014,1) is possible (give a specific example). ехина

Rectangle ABC D is in the coordinate plane. Which of the following is a valid definition of a reflection of rectangle ABC D? Every point X on ABCD is mapped to a new point X' such that each length from X toX' is the same. Every point X on ABCD is mapped to a new point X' such that the distance from X to the line of reflection is the same as the distance from X' to the line of reflection. Every point X on ABCD is mapped to a new point O X' such that the coordinates of X' are opposites of the coordinates of X. Every point X on ABCD is mapped to a new point X' such that one coordinate of X' is the same as in X and the other coordinate of X' is the opposite of the other coordinate in X.

5. Let R be a commutative ring with identity. Let f: R[x] - f(p(x)) = E, ai, where p(x) = ao+a1x + a2x² + ... + amx™m. Prove that f is a homomorphism of rings. Notice that f(p(x)) = p(1), where 1 = 1R E R. → R be defined by 4 4. Risc