If ƒ : R → R and g : R → R are both one-to-one, is f + g one-to-one? If f and g are both onto, is f + g onto?

Let A = {1, 2, 3, 4). Define the relation R on A by x R y if x ≤ y. a. List all the members of R b. Determine if R is reflexive, symmetric, anti-symmetric, transitive.

Let R be a relation from A to B and S a relation from B to A. Prove or disprove that if S of R = IdA, then S is everywhere defined. If the assertion is not true, find additional assertions that will make it true.

Let R be the relation defined on P({1,., 100}) by ARB if and only if |A n B| is even. Is R reflexive? Is R symmetric? Is R anti-symmetric? Is R transitive?