1

Logical Reasoning

Notes

Full Set

Even Integers Odd Integers

2

Prove that the sum of two odd integers is an even integer.

Statements Reasons

Deductive Reasoning : reasoning in which the conclusion is based on statements that are accepted as true.

http://www.edcollins.com/logic/index.html

Two Column Proofs: these are tools a mathematician uses to communicate his thoughts to other people. A two column proof is used to clearly explain how a mathematical or logical result is obtained.

1. Solve the equation 3(x + 4) - 5 = x + 13. Use a two column proof to explain your work.

Statements Reasons

3

Prove that the square of an odd number is always odd.

Statements Reasons

Conditions for Congruent Triangles

4

5

Refexive Property: this word is used as the reason when we want to say that a number is equal to itself.

Homework: Set up two column proofs for each of these statements.

2. The solution to 2(5x + 1) + 7 = 3(x - 2) + 43 is x = 4.

3. The solutions to are x = 4 and x = -2

4. The product of an even number with an odd number is even.

5. The square of an even number plus and odd number is always odd.

1. page 410: 3,6,9

6

Deductive Reasoning and Geometry

The perpendicular bisector theorem.

The vertical angle theorem.

Given: Prove: AB = DB

Statements Reasons

7

Given: E is the mid-point of both DB and AC

Prove: AB = CD

Statements Reasons

The isosceles triangle theorem

8

Given: BC = ED , angleOBA=angleOEF , and angleOCB=angleODE

Prove: angleBOC=angleEOD

Statements Reasons

Inductive Reasoning: reasoning in which the conclusion is based on a number of examples

9

10

Logical Terms

conjunction = and

disjunction = or

11

negation = not

a conditional statement

Statements Involving If ---, then ---

the converse

the contrapositive

12

a conditional statement

the converse

the contrapositive

a conditional statement

the converse

the contrapositive

13

a conditional statement

the converse

the contrapositive

14

15

16

17

Venn Diagrams

1. Draw a Venn Diagram for the factors of 12 and the factors of 20

18

2. Draw a Venn Diagram for the factors of 15 , 10 and 55.

3. In a classroom the only sports played are: soccer, football and hockey. 4 play none of the sports, 10 play H and F, 8 play all three sports, 14 play S and H, 13 play S and F, 30 play S, 25 play F, 31 play H.

19

4. There are 35 students in a class. 5 students take both social and English while 7 students take neither subject. 3 more students take English than social. How many take each subject?

6.

20

5.