chapter 2 take - home test alexis bacton 1. which statement is a counterexample for the following conditional? if you live in springfield, then you live in illinois. a. sara lucas lives in springfield. b. jonah lincoln lives in springfield, illinois. c. billy jones lives in chicago, illinois. d. erin naismith lives in springfield, massachusetts. 2. which conditional has the same truth value as its converse? a. if x = 7, then |x| = 7. b. if a figure is a square, then it has four sides. c. if a figure is a square, then it has four sides. d. if an angle has measure 80, then it is acute. 3. another name for an if - then statement is a ____. every conditional has two parts. the part following if is the ____ and the part following then is the ____. a. conditional; hypothesis; conclusion b. hypothesis; conditional; conclusion c. conditional; hypothesis; conditional d. hypothesis; conditional; hypothesis 4. a conditional can have a ____ of true or false. a. hypothesis b. truth value c. counterexample d. conclusion 5. when a conditional and its converse are true, you can combine them as a true ____. a. counterexample b. biconditional c. unconditional d. hypothesis 6. one way to show that a statement is not a good definition is to find a ____. a. converse b. biconditional c. conditional d. counterexample

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1. **Question 1**:
   - **Brief Explanation**: A counter - example is used to show that a conditional statement is false. If someone says “If you live in Springfield, then you live in Illinois” and we find someone like Billy Jones who lives in Springfield, Massachusetts, it is a counter - example.
   - **Answer**: C. Billy Jones lives in Chicago, Illinois. (This is incorrect as it doesn't serve as a counter - example. The correct counter - example would be someone living in a Springfield not in Illinois, like Springfield, Massachusetts. But among the given options, this question seems to have an error in the provided choices).
2. **Question 2**:
   - **Brief Explanation**: A conditional statement “If $p$, then $q$” has two parts. The “if” part is the hypothesis and the “then” part is the conclusion. In “If a figure is a square, then it has four sides”, “a figure is a square” is the hypothesis.
   - **Answer**: A. hypothesis
3. **Question 3**:
   - **Brief Explanation**: A conditional statement has a hypothesis and a conclusion. In “If $x = 7$, then $|x|=7$”, the “if” part $x = 7$ is the hypothesis and the “then” part $|x| = 7$ is the conclusion.
   - **Answer**: A. hypothesis; conclusion
4. **Question 4**:
   - **Brief Explanation**: A conditional statement can be true or false. To show it's false, we use a counter - example.
   - **Answer**: C. counterexample
5. **Question 5**:
   - **Brief Explanation**: When a conditional and its converse are both true, we can combine them as a biconditional statement.
   - **Answer**: A. biconditional
6. **Question 6**:
   - **Brief Explanation**: One way to show a statement is not a good definition is to find a counter - example.
   - **Answer**: D. counterexample

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