Sets and Relations Questions and Answers

5 Proof on relations Let R and S be relations from A to B Prove that RCS R CS

3 Proving equivalence relations Let x and y be two real numbers x y E R We define a relation R between real numbers as follows xRy IFF xy EZ In other words two real numbers are related by the relation R provided their difference in an integer Prove that R is an equivalence relation Show all your work to receive full credit

Let R S and T be relations on the set A 0 1 2 3 represented by the figures below State for each relation whether it is reflexive not reflexive symmetric not symmetric antisymmetric transitive Check all that apply No need to justify your answers but make sure you understand the properties 0 R 3 0 1 2 3 2 3 2 S Reflexive Irreflexive Symmetric Anti symmetric Transitive R S T T

Organize the steps to solve the given equation 3 x 5 29 10 Subtract 14 from each side Subtraction Property Distribute 3 to the binomial expression Distributive Property Divide both sides by 3 Division Property Combine like terms on the left side of equation Simplify