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# Mathematical Proof Techniques Quiz

### 1. Which of the following statements is always true when using a direct proof to show that if $p$ then $q$?

### 2. What method of proof is typically used to show that a statement is false by assuming the opposite of what is to be proven?

### 3. Which proof technique is especially useful for proving statements that are formulated as 'for all $n$, if $n$ is a natural number, then...'?

### 4. To prove that 'if $p$ then $q$' using the contrapositive, you must show which of the following?

### 5. Which of the following is NOT a typical step in a mathematical induction proof?

### 6. What is the main purpose of using a proof by contrapositive?

### 7. In a proof by contradiction, why is it effective to assume the opposite of what you wish to prove?

### 8. When applying mathematical induction to prove propositions involving integers, what is the purpose of the 'inductive step'?

### 9. Which proof technique employs the structure 'if $p$ is true, then $q$ is true; if $p$ is false, then $q$ can still be true'?

### 10. In which scenario is proof by contradiction NOT a suitable method?