a) Let R be a binary relation on the set of integers such that (a,b) ER if and only if b = 2a. What is the composite relation RoR? b) Let R be a binary relation on the set of ordered pairs of integers such that ((a,b),(c,d)) ER if and only if ad = bc. Show that R is an equivalence relation.

Let R be the following relation on the set of all people. R= {(a, b) : a and b share a common biological parent} Show whether or not R is an equivalence relation.

Let S be a nonempty set. Consider the relation ~ on P(S) defined by A ~ B if AUBC = S. Is the relation an equivalence relation? Explain. If yes, identify (no need to justify) the equivalence class of

Let R be the relation on the set of all mathematicians that contains the ordered pair (a, b) if and only if a and b have written a published mathematical paper together. a) Describe the relation R[2] in the context of the problem.b) Describe the relation R* in the context of the problem.c) The Erdos number of a mathematician is 1 if this mathematician wrote a paper with the prolific Hungarian mathematician Paul Erdos. The Erdos number is 2 if a mathematician didn’t write a joint paper with Erdos but wrote a joint paper with someone who wrote a joint paper with Erdos, and so on (except that the Erdos number of Erdos himself is 0). Give a definition of the Erdos number is terms of paths in R. List a name of a mathematician with number: 1, 2, and 3