Structure of proof and proof by exhaustion Quiz

1. Which of these is a valid use of proof by exhaustion?

• A. Proving a statement is true for all integers
• B. Proving a statement is true for the integers 1 to 6 by checking each
• C. Proving a statement is true from three examples that agree
• D. Proving a statement is true by checking the largest case

2. $x$ and $y$ are odd positive integers less than $5$. Which is NOT a possible value of $x+y$?

• A. $6$
• B. $4$
• C. $2$
• D. $5$

3. For integers $n$ with $2\le n\le5$, how many values of $n^3-n$ need checking in an exhaustive proof?

• A. $2$
• B. $3$
• C. $5$
• D. $4$

4. A statement holds for $n=1,2,3,4$ but fails for $n=5$. What can be concluded?

• A. It is true for all positive integers
• B. It is true except possibly for $n=5$
• C. It is false
• D. Nothing can be concluded

5. Which gives the correct values of $n^2+n$ for $n=2,3,4$?

• A. $4,9,16$
• B. $6,12,20$
• C. $6,12,18$
• D. $5,10,17$