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Topic: Question 1.5
Conf: Chapter 1, Consumer Theory, Msg: 15061
From: Martin Caley (martin.caley@economics.treasury.gov.im)
Date: 2/9/2005 06:37 AM
Question 1.5 Martin Caley MCaley martin.caley@economics.treasury.gov.im
(a) Let x be in ~(x0). Then x>=x0 and x0>=x so x is in >=(x0) intersection <=(x0).
Let x be in >=(x0) intersection <=(x0). Then x>=x0 and x0>=x so x~xo and x is in ~(x0).
(c) Assume there exists x in ~(x0)intersection >(x0). Then there exists an x such that x~x0 and x>x0, a contradiction.
(e) Clearly X = >=(x0) union x<=(x0). Take the complement.