Solutions for Boolean Functions and Computer Arithmetic

BF-1.1 The idea of this problem is to show how English phrases are translated into logical expressions. (a) f ∧ s. In English, “but” is “and” with an underlying message: The use of “but” in this way often (but not always) indicates surprise. You might say, “The animal is a fish and it lives in the water.” (F ∧W ) Or you might say “The animal is a fish but it lives on dry land.” (F ∧ L) Logic doesn’t make a fuss over surprises. (b) Either of the equivalent functions ∼(f ∨s) and (∼f)∧ (∼s). Some people think of “Neither A nor B nor . . .” as “None of A and B and . . .,” which is the first form. Other people think of “Neither A nor B nor . . .” as “Not A and not B and . . .,” which is the second form. BF-1.2 r ∧ ∼v. Same idea as the previous exercise. It may or may not be a surprise since most registered voters don’t vote, but we don’t need to know that to write it in logic notation.