21127 Lecture Notes - Lecture 10: Natural Number, Logical Connective, Burh
16 Dec 2015
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For problem #6, you don"t need to prove that addition is commutative. The point of the question is to see whether you can interpret the sets appropriately. The only algebraic issue comes up in part (d). For problem #2, you shouldn"t need to write out 12 cases. Furthermore, you should not be saying something about maximum or minimum values. In fact, any meaningful de nition of max or min would be stated in terms of an inequality, which is what you are trying to deduce, anyway. Just take an arbitrary element of a, and write down something you know about such an element, in terms of a few inequalities. Manipulate those to conclude the element is in b, as well. Important observation: the phrase such that comes always and only after an quanti cation. Some bad examples: x. x > 7, y z, z > 2. z2 > 4, w z. w2 = t. t n.
