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Unit 3 Logic

G.1 The student will construct and judge the validity of a logical argument consisting of a set of premises and a conclusion. This will include a) identifying the converse, inverse, and contrapositive of a conditional statement; b) translating a short verbal argument into symbolic form; c) using Venn diagrams to represent set relationships; and d) using deductive reasoning.

Notes Day 1

Conditional Statements (Converse, Inverse and Contrapositive)

Vocabulary

Term Definition Conditional Statement S________________ that can be w_________________ in “if…, then”

form Hypothesis Part of a c_________________ statement that f________________ “if” Conclusion Part of a conditional s__________________ that follows “then” Negation D_______________ of a s____________________ formed by adding or

removing the word ______________ from a statement Negate To add or remove the word __________ from a statement to change its

truth value from true to __________________ or from false to __________________

Converse S____________________ formed from a c___________________ statement by s__________________ the h__________________ and c___________________

Inverse S__________________ formed from a c_________________ statement by n__________________ the h__________________ and c___________________

Contrapositive S__________________ formed from a c_________________ statement by s__________________ AND n__________________ the h__________________ and c___________________

Biconditional Statement combining a c____________________ statement and its c________________, using the phrase “if and o____________ if”

Today I will construct the converse, inverse and contrapositive of a conditional statement, so that I judge the validity of logical arguments. I will know that I have it when I can correctly identify the inverse, converse and contrapositive of a conditional statement on 3 out of 4 conditional statements on the exit ticket.

Examples

Conditional Statements

1. Conditional Statement: _________________________________________________

Inverse:______________________________________________________________

Converse: ____________________________________________________________

Contrapositive:_________________________________________________________

2. If you eat breakfast, then you will feel better at school.

Inverse:______________________________________________________________

Converse: ____________________________________________________________

Contrapositive:_________________________________________________________

3. If two lines are perpendicular, then they form right angles.

Inverse:______________________________________________________________

Converse: ____________________________________________________________

Contrapositive:_________________________________________________________

4. If two angles are supplementary, then their sum is 180° .Inverse:______________________________________________________________

Converse: ____________________________________________________________

Contrapositive:_________________________________________________________

VDOE Released Test Items (2014-15)

Notes Day 2

Valid Arguments

There are three valid arguments:

1. ________________________________2. ________________________________3. ________________________________

Contrapositive:

Syllogism:

Detachment:

Today I use deductive reasoning, so that I can determine the validity of arguments that use contrapositive, syllogism and detachment. I will know that I have it when I can correctly identify those set relationships on 9 out of 12 problems on the scavenger hunt.

Examples

1. If I go to the movie, then I’ll eat popcorn.

If I eat popcorn, then I’ll enjoy the movie.

A. Conclusion? ______________________________________________

B. Law of logic? _____________________________________________

2. If a figure is a square, then it is a rectangle.

Quadrilateral ABCD is a square.

A. Conclusion? ______________________________________________

B. Law of logic? _____________________________________________

3. If I go to the movie, then I’ll eat popcorn.

If I eat popcorn, then I’ll enjoy the movie.

A. Conclusion? ______________________________________________

B. Law of logic? _____________________________________________


If a figure is a rectangle, then it has 4 right angles.

A. Conclusion? ______________________________________________

B. Law of logic? _____________________________________________

Notes Day 3

Venn Diagrams

And ______ Must be both

Or ______ Inclusive of all

Only ______________________

Today I use Venn diagrams to represent set relationships, so that I can make correct premises and conclusions. I will know that I have it when I can correctly identify those set relationships on 7 out of 10 problems on the exit ticket.

How many students are taking a foreign language? _____

How many are taking German and Spanish? _____

How many are taking French but not German? _____

How many are taking Spanish and French, but not German? _____

How many students are taking all three languages? ______

Today I use Venn diagrams to represent set relationships, so that I can make correct premises and conclusions. I will know that I have it when I can correctly identify those set relationships on 7 out of 10 problems on the exit ticket.

Practice

Homework

Day 1: Conditional Statements

Write your own conditional statement. Then write the inverse, converse and contrapositive of that statement.


Inverse:______________________________________________________________

Converse: ____________________________________________________________

Contrapositive:________________________________________________________


Inverse:______________________________________________________________

Converse: ____________________________________________________________

Contrapositive:_________________________________________________________

Homework

Day 2: Valid Arguments

Read each argument, determine the conclusion to the argument and what law of logic justifies the conclusion.

1. If an animal is a pig, then it is a mammal.

Leon is a pig.

A. Conclusion? ______________________________________________

B. Law of logic? _____________________________________________

8. If a quadrilateral is a square, then it has four congruent sides.

Quadrilateral ABCD has four congruent sides.

A. Conclusion? ______________________________________________

B. Law of logic? _____________________________________________


If a figure is a rectangle, then it has 4 right angles.

A. Conclusion? ______________________________________________

B. Law of logic? _____________________________________________

10. If a man is wealthy, then he buys a mansion.

If a man can buy a mansion, then he can hire a housekeeper.

A. Conclusion? ______________________________________________

B. Law of logic? _____________________________________________

Homework Day 3: Venn Diagrams

Use the following information to fill in the Venn Diagram below.

100 people were asked if they liked Math, Science, or Social Studies. Everyone answered that they liked at least one.

56 like Math 18 like Math and Science

43 like Science 10 like Science and Social Studies

35 like Social Studies 12 like Math and Social Studies

6 like all three subjects

1.How many people like Math only? _____

2.How many people like Science only? _____

3. How many people like Social Studies only? _____

Math Science

Social Studies

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