11.3. Without Loss of Generality (w.l.o.g.)

Try these first

1. 1.

   What is a counterexample?

   Hint

   Think of an example that disproves a general claim.

2. 2.

   Explain proof by cases in one sentence.

   Hint

   No hint provided

3. 3.

   What is a counterexample?

   • An example that proves a statement true
   • An example that disproves a statement
   • An irrelevant example

   Hint

   Think of examples that are the opposite of what the statement claims.

4. 4.

   Using w.l.o.g. means choosing a particular case that constrains the proof.

   • True
   • False

   Hint

   Consider how this simplifies your reasoning.

5. 5.

   Using w.l.o.g., prove that for any two real numbers x and y, if x + y is odd, one of them must be even.

   Hint

   Explore the definitions of odd and even carefully.

6. 6.

   Show that the product of any two odd integers is odd.

   Hint

   Factor out to see the result!