Reasoning, Logic, and Venn Diagrams
Test your knowledge. You have 3 attempts.
1. Consider the statement: "If an angle measures 90°, then it is a right angle." Identify the hypothesis.
2. What is the converse of the statement "If a figure is a square, then it has four right angles"?
3. Using inductive reasoning, find the next item in the pattern: 3, 6, 12, 24, ...
4. Which of the following is a counterexample for the statement "If an animal has four legs, then it is a dog"?
5. Given: "If two angles form a linear pair, their measures sum to 180°. $\angle1$ and $\angle2$ form a linear pair." What is the conclusion by the Law of Detachment?
6. Given: "If you hike to the Mill Mountain Star, you get a great view." and "If you get a great view, you will be amazed." Conclude with the Law of Syllogism.
Use the Venn diagram below for questions 7 and 8.
7. How many students are in Band but NOT Chorus?
8. How many students are in the intersection of the sets, shown as
Band $\cap$ Chorus?
9. A biconditional is true if the original conditional and its converse are both true. Which statement can be written as a true biconditional?
10. Let $p:$ "It is sunny" and $q:$ "I will go to the park."
Which symbolic statement represents "If it is sunny, then I will NOT go to the park"?