• \neg (x < n < y) is not equivalent to x\ge n \ge y. The correct solution uses De Morgan's law, on the expanded version x<n \land n < y.

• Generally, do study DeMorgan's law. Can't hurt. Also know how to rewrite the implication using \lor and \neg.

• Always be mindful of what arguments predicates might take, and do not omit them: Say P(x) when you mean a predicate P evaluated for x. The x is not optional, and points will get taken off if you skip it.

• Domains of quantifiers don't change if you pull a negation sign through them.
• When I said "try to use equivalences", I meant "you should be able to do this using equivalences." Truth tables will not help you much going forward in the class, as in, they won't get you any points.
• D=\mathbb Z and D=\{ \mathbb Z \} are not the same thing. In one case, the set D is the set of all integers. In the other, it's the set consisting of the set of all integers. Suppose you have an apple and an orange and a pear (each representing an integer). Then the first is a bag containing all three. The second is a bag containing a bag containing all three.

Also, the grader was lenient on questions of form. That won't be the case on future homework (or quizzes). Messy solutions will get points taken off.

Teaching/DiscreteMathSpring2011/HomeworkSet02/CommonMistakes (last edited 2011-04-23 18:30:39 by AndreasKloeckner)