Logical arguments

12 questions

1. The sum of any two integers is always __________.
2. If n and m are integers which of these are always even?
3. How could we generalise the difference between any two consecutive multiples of 10?
4. A rational number can be written in the form __________.
5. Which of these numbers are rational?
6. Alex writes the conjecture "All numbers of the form n^2 where n is an integer are positive". There is a counterexample to this when n=___?
7. Which is the correct opposing statement to "All basketball players are tall"?
8. Which is the correct opposing statement to "All integers greater than -1 are positive"?
9. Which is the correct opposing statement to "All multiples of 10 are even"?
10. Which is the correct opposing statement to "If a and b are even then a+b is even"?
11. Arrange these steps for the proof that "For any integer a if a^2 is even then a is even" into the correct order.
12. Arrange these steps for the first half of the proof that "The number \sqrt 2 is irrational" into the correct order.

License: OGL