MATH 241 Lecture 10: Relations and their Properties
12 Feb 2019
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Anti - reflexive : x rx is false for all. X ry implies y rx for all x , y e a. Anti - symmetric : for all: y. Transitive : if x ry and y r2 , then x rz for all: y , z. Let a be the set of divisors of. 12 . construct the relation defined by { ( a , b) e a x a : at b } It , 12) , ( 2,21 , ( 2,4 ) , 12,6 ) , I 12 , 1213 what properties does this set have ? reflexive , transitive , and anti. I defined by a rb if a - b is divisible by 7 . We say a is congruent to b modulo 7 and write. What properties does r satisfy ? (cid:8869) it"s reflexive , symmetric , and transitive. L et r be the relation on pc it , 2,33 ) defined by arb if.
