7. Suppose that you have 2 two-bit bit strings a and b. Think of a as a1 a0 and b as b1 b0. 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, b0, and b1 such that L is true if and only if ab. Forexample,Lshouldbetrue(T)whena=10andb=11,Lshouldbefalse 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.