MAT-3110 Midterm: MATH 3110 App State Fall2009 Test1 answer key

• School: App State
• Department: Mathematics
• Course: MAT-3110
• Professor: All

Document Summary

September 30th, 2009: (18 points): de ne a binary operation on z, as follows x y = x + xy + y (for all x, y z). So, for example, ( 2) ( 3) = ( 2) + ( 2)( 3) + ( 3) = 1. (a) show is associative. Since the two expressions match, we have that (x y) z = x (y z). Therefore, is associative. (b) show 0 is the identity for . Let x z. x 0 = x + x0 + 0 = x and 0 x = 0 + 0x + x = x. Recall that p(s) = {a | a s} is the power set of s (i. e. the set of all subsets). (a) which of the following are true? i. ii. The empty set is a subset of s. thus it is an element of the power set of. In fact, the empty set is a subset of every set. v.