Mathematical Proof/Appendix/Answer Key/Mathematical Proof/Introduction/Notation

1. Use set theory notation
   1. $P\cap L$, where P is the set of all people and L is the set of all things with two legs.
   2. $M-G$, where M is the set of all mythological creatures and G is the set of all things that are Greek.
   3. $A\cap B-C$, where A is the set of all pies, B is the set of all things with pudding in them, and C is the set of all things with cream on the top.
2. Venn Diagrams
3. Negated statements
   1. $\mathrm{\exists }x\in A:\mathrm{\forall }y\in B,\mathrm{\neg }P(x,y).$
   2. There is a quick, brown fox that does not jump over any lazy dog.