Combining what we have already talked about!

Conditional Statements: If_______________ then _____________________.Hypothesis Conclusion

Change the following statement into an if then statement:

Ex: A number is divisible by 9 is also divisible by 3.

Answer: If a number is divisible by 9 then it is also divisible by 3.

Ex: Two points are collinear if they lie on the same line.

Answer: If two points are collinear then they lie on the same line.

TRUTH TABLES: ConjunctionConstruct a basic Truth Table for the CONJUNCTION

(AND) argument:

Ex: I love ice cream and I love to go hiking P Q P ^ Q

T T

T F

F T

F F

I love ice cream and I love to go hiking I love ice cream and I do not love to go hiking I don’t love ice cream and I love to go hiking

I don’t love ice cream and I don’t love to go hiking

P Q

F

T

F

F

Condition Argument Workspace T or F?

1. P is true and Q is true P ^ ~Q

2. P is false and Q is true ~P ^ ~Q

3. P is false and Q is false P ^ Q

4. P is false and Q is true ~P ^ Q

5. P is true and Q is false ~P ^ Q

6. P is true and Q is false P ^ ~Q

P is true and Q is false

P is true and Q is false

P is false and Q is false

P is true and Q is true

P is false and Q is false

P is true and Q is true

F

FF

FT

T

Apply these changes to the condition.

TRUTH TABLES: Disjunction Construct a basic Truth Table for the DISJUNCTION

(OR) argument:

Ex: the shirt has flowers or the shirt is blue P Q P v Q

T T

T F

F T

F F

The shirt has flowers or the shirt is blue

The shirt has flowers or the shirt is not blue The shirt does not have flowers or the shirt is blue

The shirt does not have flowers or the shirt not is blue

P Q

T

T

T

F

Condition Argument Workspace T or F?

1. P is true or Q is false ~P v Q

2. P is false or Q is false P v ~Q

3. P is false or Q is true ~P v ~Q

4. P is false or Q is false P v Q

5. P is true or Q is true ~P v ~Q

6. P is true or Q is true P v ~Q

P is false or Q is false

P is false or Q is true

P is true or Q is false

P is false or Q is false

P is false or Q is false

P is true or Q is false

F

TT

FF

T

TRUTH TABLES: ConditionalConstruct a basic Truth Table for the CONDITIONAL

(If…Then) argument:

P Q P → Q

T T

T F

F T

F F

Ex: If you participate in class then you will get extra points.

If you participate in class then you get extra points.

If you participate in class then you do not get extra points.

If you do not participate in class then you get extra points

P Q

T

F

T

T If you don’t participate in class then you don’t get extra points

Condition Argument Workspace T or F?

1. P is true and Q is true ~P → ~Q

2. P is true and Q is false P → ~Q

3. P is false and Q is false ~P → Q

4. P is true and Q is false P → Q

5. P is false and Q is false P → Q

6. P is true and Q is true ~P → Q

P is false or Q is false

P is true or Q is true

P is true or Q is false

P is true and Q is false

P is false and Q is false

P is false or Q is true

T

TF

TF

T

Homework:

*Pick 5 of the Conditional Statements on your pink sheet. Convert all of them into converse, inverse, and contrapositive.

Also TRY to change those Conditional Statements into a code (Use the symbols on the second page of the packet!)

Due: 9/10/2012

P Q P Q

T T T

T F F

F T T

F F T

TRUTH TABLES for the CONVERSE of a CONDITIONAL STATEMENT

Q P Q P

T

F

T

F

T

T

F

F

T

T

F

T

What do you notice about the TRUTH TABLE of a CONDITIONAL & its CONVERSE?

P Q P Q

T T T

T F F

F T T

F F T

~P ~Q ~P ~Q

F

T

F

T

F

F

T

T

T

T

F

T

TRUTH TABLES for the INVERSE of a CONDITIONAL STATEMENT

What do you notice about the TRUTH TABLE of a CONDITIONAL & its INVERSE?

P Q P Q

T T T

T F F

F T T

F F T

~Q ~P ~P ~Q

F

T

F

T

F

F

T

T

T

F

T

T

TRUTH TABLES for the CONTRAPOSITIVE of a CONDITIONAL STATEMENT

What do you notice about the TRUTH TABLE of a CONDITIONAL & its CONTRAPOSITIVE?

Condition Argument Workspace T or F?1. P is true and Q is true Converse

2. P is true and Q is false Inverse

3. P is false and Q is false Converse

4. P is true and Q is false Contrapositive

5. P is false and Q is false Inverse

6. P is true and Q is true Contrapositive

PRACTICE: (Homework if not finished in class)

For questions 7-8, change statements into code:

7. If I eat 1 pound of candy then I will get sick.8. If Joy goes to the movies then Joy eats popcorn or Joy eats kettle corn.

Q = true and P = true T