Problem 2: Define S = {0, 1} and define the operations 4, O by the following tables: 1 1 0 and 0 1. 1 1 1 1 1 (That is, 0 O0 = 0, 01=100 = 101 = 1,0 00 = 0 01=100 = 0 and 1 01= 1.) Using this definition (do not use the Boolean algebra properties; this is a piece of proving this is a Boolean algebra, so we don't know they're true yet): (a) prove that 1 is an identity element for O and is an identity element for O (b) Defining 0 = 1 and 1 = 0 , prove that Va E S, a Ðā = 0 and a O a = 1 .

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