CHAP 1: LOGIC

“If it was so, it might be: and if it were so, it would be; but as it isn’t, it ain’t.

That’s logic”-Lewis Carroll, author of

Alice in Wonderland

PART 1: STATEMENTS & STANDARD FORMS

Statement:Any declarative sentence that is

either true (T) or false (F) but not both

T or F are called truth value of the statement

Statements use lower case letters like p, q, r

EXAMPLES OF STATEMENTS

1. Let p be the sentence “Santa is Jolly”

2. Let q be the sentence “ Christmas is on July 4th”

Number 1 & 2 are statements bc we can assign to them a truth value

Is the following a statement? “Solve the following for X”

THE ABOVE is a COMMAND

MORE WORDS

Negation

The statement whose truth value is

the opposite of the truth value of p

The symbol for a negation is ~

When you have ~ p it is read as “not

p”

EXAMPLES OF NEGATIONSTATEMENTS

1. Let p be the sentence “Santa is Jolly”

What would be a ~p ?

“Santa is not jolly”

2. Let q be the sentence “ Christmas is on July

4th”

What would be a ~q ?

“Christmas is not on July 4th”

Notice that these negations are also

statements that can be given truth values

TRUTH TABLES

Used to show the truth values for different statements

Each Column represents a statement And the rows below show the different truth

values possible

P ~ P

T F

F T

Q ~ Q

QUICK NOTE

The negations of statements will be referred to

as being in STANDARD FORM

Example:

the standard form of the negation of the

statement “Santa is jolly” is the statement “Santa

is not jolly”

The standard form of the negation of the

statement “ Texas is not a state” is …….

“Texas is a state”

YOUR TURN TO TRY

Write a negation in standard for each of the statements

1.a: Dallas is the capital of Oklahoma2.b: An orange is a fruit3.c: An apple is not Blue

CHECK YOUR ANSWERS

1. ~a: Dallas is not the capital of

Oklahoma

2. ~b: An orange is not a fruit

3. ~c: An apple is Blue

NOW LETS GIVE THE EACH STATEMENT A TRUTH VALUE

a __________~ a _________

c __________~ c _________

b __________

~ b __________

1. a: Dallas is the capital of Oklahoma2. b: An orange is a fruit3. c: An apple is not Blue

1. ~a: Dallas is not the capital of Oklahoma

2. ~b: An orange is not a fruit

3. ~c: An apple is Blue

ANOTHER NEW WORD

Conjunction

Is putting two statements together

using the word and

The symbol for and is ^

Example p ^ q is read as “p and q”

This statement is true ONLY if BOTH

are true

EXAMPLES OF CONJUNCTION STATEMENTS

1. Let p be the sentence “Santa is Jolly”

2. Let q be the sentence “ Christmas is on July

4th”

3. Let r be the sentence “George Washington

was the first U.S. President:

Write a conjunction of p and q

Write a conjunction of p and r

Write a conjunction of q and r

CHECK YOUR ANSWERS

Santa is jolly and Christmas is on July

4th

Santa is jolly and George Washington

was the first U.S. President

Christmas is on July 4th and George

Washington was the first U.S.

President

WHAT ARE THE TRUTH VALUES?

Santa is jolly and Christmas is on July 4th

FALSE! FALSE! Santa is jolly and George Washington was

the first U.S. President

TRUE! TRUE! TRUE!

Christmas is on July 4th and George

Washington was the first U.S. President

FALSE!!! FALSE!

A GENERAL TRUTH TABLE FOR P ^ Q

p q p ^ q

ONE LAST WORD

DISJUNCTION

Is putting two statements using the word

or

The symbol for or is v

Example p v q is read as “ p or q”

The statement is true IF and ONLY IF at

LEAST ONE of p and q is TRUE

EXAMPLES OF DISJUNCTION STATEMENTS

1. Let p be the sentence “Santa is Jolly”

2. Let q be the sentence “ Christmas is on July

4th”

3. Let r be the sentence “George Washington

was the first U.S. President:

Write a disjunction of p and q

Write a disjunction of p and r

Write a disjunction of q and r

CHECK YOUR ANSWERS

Santa is jolly or Christmas is on July 4th

Santa is jolly or George Washington

was the first U.S. President

Christmas is on July 4th or George

Washington was the first U.S.

President

WHAT ARE THE TRUTH VALUES?

Santa is jolly or Christmas is on July 4th

TRUE! Santa is jolly or George Washington was

the first U.S. President

TRUE! TRUE! TRUE!

Christmas is on July 4th and George

Washington was the first U.S. President

TRUE! TRUE! TRUE!

WHAT ABOUT………..?????

~ p v q

A GENERAL TRUTH TABLE FOR P V Q

p q p v q

NOW TIME TO PUT IT ALL TOGETHER

Given Statements

a: Abraham Lincoln was the 16th U.S.

president

b: A lemon is tart

c: Valentines Day is in December

QUESTIONS

1. a ^ b2. a v c3. ~a ^ b4. ~ c v ~ a5. The truth value for # 1 is ____________6. The truth value for # 2 is ____________7. The truth value for # 3 is ____________8. The truth value for # 4 is ____________