10.1.3.3.1. Using Proof by Contradiction for Single Proposition

Try these first

1. 1.

   What is proof by contradiction?

   Hint

   Consider how assuming the opposite can reveal inconsistencies.

2. 2.

   Give an example of proof by contradiction.

   Hint

   Think about rational numbers that result from fractions.

3. 3.

   What does proof by contradiction involve?

   • Assuming a statement is true
   • Assuming a statement is false
   • Directly proving the statement

   Hint

   Reflect on the logical sequence of proving truths.

4. 4.

   True or False: Proof by contradiction can be used only for implications.

   • True
   • False

   Hint

   Consider its application beyond just implications.

5. 5.

   Prove that if the sum of two irrational numbers can be rational, provide an example.

   Hint

   Look at properties of numbers and their sums.

6. 6.

   Demonstrate that there exists no smallest positive rational number.

   Hint

   Reflect on the structure of rationals and their properties.