3. Let X be a set7 and let l and :2 be two binary relations on X. Dene the lemicogmphic binary relation fl as follows: for any :73, y E X , we have :5 EL if and only if at least one of the following two conditions holdszl. ZL' >1 LU o a; N1 y and a; :2 y. [If :1 and :2 capture how a decision maker feels about different aspects of a decision, then :1; is one way of combining them: use aspect 1 to make decisions, but if aspect 1 does not make the decision easy, then use aspect 2 to break ties] Explain why each of the following is true: (a) If any 6 X have :1: :L y, then :1: :1 y. (b) :L is complete if both :1 and :2 are complete. (0) L is transitive if both l and :2 are transitive. [Hintz part (a) of this question and parts (be) of the previous question may be helpful] >L is a preference relation if both :1 and :32 are preference relations. N (d) (e) If :2 is exactly :1, then L is exactly :1- (f) If :2 is exactly jl (see question 2(a)), then :L is exactly a