4023s09ex2

# 4023s09ex2 - Name: Exam 1 Instructions. Answer each of the...

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Name: Exam 1 Instructions. Answer each of the questions on your own paper, and be sure to show your work so that partial credit can be adequately assessed. Credit will not be given for answers (even correct ones) without supporting work. Put your name on each page of your paper. 1. [15 Points] Recall that a relation on a set A is (R) re±exive if aRa for all a 2 A , (S) symmetric if whenever aRb , then bRa , (AS) antisymmetric if whenever aRb and bRa , then a = b , (T) transitive if whenever aRb and bRc , then aRc . (a) Which of the above properties must be satisﬂed for the relation R to be a partial order ? (b) Which of the above properties must be satisﬂed for the relation R to be an equivalence relation ? (c) Determine whether each of the following relations on the integers Z is (1) a partial order, (2) an equivalence relation, or (3) neither. i. The relation R deﬂned on Z by nRm if and only if n ¡ m is even. ii. The relation R deﬂned on Z by nRm if and only if n ¡ m is odd.

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## This document was uploaded on 12/28/2011.

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4023s09ex2 - Name: Exam 1 Instructions. Answer each of the...

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