Determine if the following sets with operations are groups: (a) R with the operation given by r* y = -1- y. (b) The subset of R³ given by H = {(r, y, 2) E R° | x + y + z = 0}, with the operation (x, y, 2) + (a, b, c) = (r+a, y+ b, z + c).

Given the set A={1,2,3,4} and the function ff:A⟶A, where f={(1,2),(2,1),(3,4),(4,2)}, which of the following is f2=f∘f ? Group of answer choices   {(1,1),(2,2),(3,2),(4,1)} {(1,2),(2,4),(3,3),(4,1)} {(1,1),(2,1),(3,2),(4,3)} {(1,1),(2,1),(3,2),(4,2)}

What are the coordinates of the point on the directed line segment from (−1,−8)(−1,−8) to (5,−2)(5,−2) that partitions the segment into a ratio of 1 to 2?

discrete math