Question

reasoning in mathematics unit 2 & unit 3 review worksheet topics: inductive & deductive reasoning | sets & venn diagrams name: date: unit 2: inductive and deductive reasoning 1. identify whether the reasoning is inductive or deductive: every time the sun rises, it rises in the east. therefore, the sun always rises in the east. 2. identify whether the reasoning is inductive or deductive: all rectangles have four sides. a square is a rectangle. therefore, a square has four sides. 3. use inductive reasoning to predict the next number: 2, 4, 8, 16, 4. use inductive reasoning to predict the next number: 1, 4, 9, 16, ___ 5. a pattern shows that the sum of two even numbers is always even. what type of reasoning is this? 6. if all mammals are warm - blooded and dogs are mammals, what can you conclude? 7. identify the hypothesis and conclusion: if a figure is a square, then it has four equal sides. 8. is the following argument valid? all birds have wings. penguins have wings. therefore, penguins are birds. unit 3: sets and venn diagrams 9. let a = {1, 2, 3, 4} and b = {3, 4, 5}. find a ∪ b. 10. let a = {1, 2, 3, 4} and b = {3, 4, 5}. find a ∩ b. 11. find a - b using the sets above. 12. let u = {1,2,3,4,5,6} and a = {2,4,6}. find a. 13. true or false: a ∩ b includes elements found in both sets. 14. true or false: a ∪ b includes only elements common to both sets. 15. list the elements in the set of even numbers less than 10. 16. write the set {2, 4, 6, 8} using set - builder notation. 17. how many elements are in the set {a, e, i, o, u}? 18. draw a venn diagram to show a ∩ b.

Explanation:

Answer:

1. Inductive
2. Deductive
3. 32
4. 25
5. Inductive
6. Dogs are warm-blooded.
7. Hypothesis: A figure is a square; Conclusion: It has four equal sides.
8. Invalid
9. $\{1, 2, 3, 4, 5\}$
10. $\{3, 4\}$
11. $\{1, 2\}$
12. $\{1, 3, 5\}$
13. True
14. False
15. $\{2, 4, 6, 8\}$
16. $\{x \mid x \text{ is an even integer and } 2 \le x \le 8\}$
17. 5
18. Two overlapping circles with the intersection shaded.