Section  Problem  Notes


1.4  36

1.7  38  Clearly show why your counterexample works. Also, read the problem carefully so you do not come up with a false counterexample.

2.1  30  Prove your conclusion.

2.2  16e  Use a "set containment proof". Your proof should contain phrases like "Let x∈FOO", "by the definition of union", "thus FOO⊆FERZLE", etc.

2.3  20  N is the set of natural numbers ({0, 1, 2, ...}). Also, when part c says "different than the identity", it means it cannot always map a number to itself, regardless of what the function looks like. So functions like f(x)=⌊x⌋ or f(x)=2*(x/2) don't count.

 36  Make sure you clearly indicate which answer is which.

2.4  4ad

 16b

 26bh  Do not give a recursive formula. I should be able to determine a_{100} by just plugging in 100, for instance. Assume the first term is a_{1.
} 
 32c  Make sure to show your work.

 34b  Make sure to show your work.

 40  Make sure to show your work. 