Unit 1 Study Tool

Unit 1 Quiz Study Guide

Reasoning, Logic, & Venn Diagrams

Test your knowledge. You have 3 attempts.

Attempt 1 of 3

1. Let $p$ be 'The sun is shining' and $q$ be 'It is raining.' Which correctly translates $p \land \sim q$?

A. If the sun is shining, then it is not raining. B. The sun is shining and it is not raining. C. The sun is shining or it is not raining.

2. What is the contrapositive of: "If a polygon has three sides, then it is a triangle."?

A. If a polygon is a triangle, then it has three sides. B. If a polygon does not have three sides, then it is not a triangle. C. If a polygon is not a triangle, then it does not have three sides.

3. Which law allows you to conclude: "If I study, then I will be happy" from "If I study, I'll pass" and "If I pass, I'll be happy"?

A. Law of Detachment B. Inductive Reasoning C. Law of Syllogism

4. The conditional statement $p \rightarrow q$ is only false when...

A. p is True, q is True B. p is False, q is False C. p is False, q is True D. p is True, q is False

5. Which of the following pairs of statements are logically equivalent?

A. A conditional and its converse. B. A conditional and its inverse. C. The converse and the inverse. D. The contrapositive and the inverse.

6. Which is a valid counterexample to the statement "All birds can fly"?

A. A bat can fly. B. A penguin is a bird. C. A penguin cannot fly. D. An airplane can fly.

7. In a Venn diagram, what does the notation $A \cup B$ represent?

A. Elements in both A and B (intersection). B. All elements in A, B, or both (union). C. Elements in A but not in B. D. All elements not in A (complement).

8. Given: "If it is Saturday, then I do not go to school." Today is Saturday. What can you conclude?

A. It is not Saturday. B. I do not go to school. C. I go to school. D. No conclusion can be made.

9. In a class of 50 students, 28 play basketball, 22 play soccer, and 10 play both. How many students play neither sport?

10. A biconditional statement ($p \leftrightarrow q$) is true only when...

A. The original conditional is true. B. The contrapositive is true. C. The conditional and its converse are true. D. The inverse is false.