17.7.1. Universally Quantified Statement

Try these first

1. 1.

   What is a universally quantified statement?

   Hint

   Think about statements that include 'for all'.

2. 2.

   State the pigeonhole principle in your own words.

   Hint

   Consider how items might be distributed.

3. 3.

   What is a universally quantified statement?

   • A statement that applies only to specific cases
   • A statement that applies to some elements
   • A statement that applies to all members of a set

   Hint

   Focus on the term 'universally'.

4. 4.

   True or False: In the pigeonhole principle, if you have 10 items and 5 holes, at least one hole must contain more than two items.

   • True
   • False

   Hint

   Think about how you'd distribute the items.

5. 5.

   Construct an example using integers 1-20, applying the pigeonhole principle to select numbers summing to a multiple of 10.

   Hint

   Think of the digits when adding.

6. 6.

   Seek patterns within any integer set, using the example of k=4 to show that a sequence created has values composed only of 0s and 1s.

   Hint

   Focus on constructing sequences with repeating patterns.