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Question 10 Decide, giving reasons, whether in Question is: (a) reflexive: birreflexive: Ich symmetric (d) asymmetric (e) antisymmetric f) transitive Question 11 Let a relation be represented by the following matrix 1OOOOO IIIIOOO 1011010 M-)-100 100 I10IO. 01 01101 IIIIIO Determine whether Ris (a) reflexive: (b) irreflexive: Ich symmetric (d) asymmetric le) antisymmetric f) transitive GIVE REASONS FOR YOUR ANSWERS1 Question 12 Equivalence relations are relations for which it is possible to see related elements similar in some or other sense. Decide for each of the following relations whether or not it Is an equivalence relation. Give full reasons. If it is an equivalence relation, prethe equivalence classes a) Let a and be integers, Define ait and only if the product of aand bis ever (b) Let a and be sets of natural numbers. Define Rhif and only ife and are disjoint that is an c) Let A = (the real numbers). Define abf and only if his an integer