10.1.1. Proof Strategies-I

Try these first

1. 1.

   What is a direct proof?

   Hint

   Consider its definition in the context of implications.

2. 2.

   Provide an example of a universally quantified statement.

   Hint

   Think about properties of even and odd numbers.

3. 3.

   What does a direct proof do?

   • Assumes Q is true
   • Assumes P is true
   • Has no assumptions

   Hint

   Think about how direct proofs relate to implications.

4. 4.

   Is proof by contrapositive valid for proving implications?

   • True
   • False

   Hint

   Recall the connection between a statement and its contrapositive.

5. 5.

   Given the statement 'If n is a multiple of 4, then n² is a multiple of 16', prove it using a direct proof.

   Hint

   Start by expressing n in terms of k.

6. 6.

   Prove 'if the product of two integers is odd, then both integers must be odd' using proof by contrapositive.

   Hint

   Identify how even and odd integers interact when multiplied.