1) Consider bit strings of 3 bits b2 b1 b0. Develop a proposition R expressed in terms of b0, b1, and b2 which is true (T) for such a bit string if and only if b2 b1 bo b0 b1 b2, i.e., if the bit string b2 b1 bO is equal to its reverse. For example, R should be true(T) for bit string 010, but false F for bit string 001. Simplify you proposition as much as possible using the replacements laws of propositional logic. Suppose that you have 2 two-bit bit strings aand b. Think of a as ala0 and b as b1b0. So a(and, similarly b) represent the natural numbers 0, 1, 2, and 3 as the bit strings 00,01,10, and 11, respectively. Design a proposition L in terms of a0, a1, bo, and b1 such that L is true if and only if a s b. For example, L should be true (T) when a 10 and b 11, L should be false when a 01 and b-00, and L should also be true when a = 01 and b-01. Simplify you proposition as much as possible using the replacements laws of propositional logic. Suppose that you have 2 two-bit bit strings a and b. Think of a as ala0 and b as b1b0. So a.and b represent the numbers 0, 1, 2, and 3 as the bit strings 00, 01, 10, and 11, respectively. Design 2 propositions in terms of ao, a1, bo, and b1 that "implement" the function max(O, a-b). So for example max(0, 3-0) 3 and max(0,1-2) 0. Notice that you need 2 propositions since max ranges from 0 to 3. Simplify your propositions as much as possible using the replacement laws. 2)