Symbolic Logic

Objectives

• Determine if a sentence or question is a statement or not.

• Write a sentence that represents the negation of a given statement.

• Rewrite a statement in symbolic form (defining the symbols used).

• Rewrite a symbolic statement in word form.

Vocabulary

• Statement• Compound statement• Negation• Conjunction• Disjunction (inclusive or)• Conditional (implication)• Hypothesis (premise)• Conclusion

• Statement:

• Compound statement:

a statement is a sentence that is either true or false

a statement that contains one or more simpler statement

(not, and, or, if . . . then, only if, if and only if)

Determine which of the following are statements.

)1)(1(1.4 2 xxx

653.1

2. Solve the equation 2x + 5 = 3.

3. x2 + 1 = 0 has no solution.

number?rationala2Is.5

• Negation:

• Conjunction:

• Disjunction:

• Conditional:

denial of a statement (symbol: ~)

and (symbol: ^)

Connectives

or – inclusive or (symbol: V)

if . . ., then (symbol: →)

Write the statement that represents the negation:

1. His car is not new.

2. Some buildings are earthquakeproof.

3. All children eat candy.

4. I never cry in a movie theater.

Negation Summary

Statement Negation

Some p are q. No p are q.

All p are q. Some p are not q.

No p are q. Some p are q.

Some p are not q. All p are q.

Using the symbolic representations

p: The car costs $40,000.q: The car goes 140 miles

per hour.r: The car is red.

express the following compound statements in symbolic form.1.The car is red, goes 140 mph, and

does not cost $40,000.

Using the symbolic representations

p: The car costs $40,000.q: The car goes 140 miles

per hour.r: The car is red.

express the following compound statements in symbolic form.2.If the car does not cost $40,000, it

does not go 140 mph.

Using the symbolic representations

p: The car costs $40,000.q: The car goes 140 miles

per hour.r: The car is red.

express the following compound statements in symbolic form.3.The car is red and it does not go 140

mps or cost $40,000.

Using the symbolic representations

p: The car costs $40,000.q: The car goes 140 miles

per hour.r: The car is red.

express the following compound statements in symbolic form.4.All red cars go 140 mph.

Using the symbolic representations

p: I am an environmentalist.q: I recycle my aluminum

cans.r: I recycle my newspapers.

express the following compound statements in symbolic form.

prq .1

Using the symbolic representations

p: I am an environmentalist.q: I recycle my aluminum

cans.r: I recycle my newspapers.

express the following compound statements in symbolic form.

)(~.2 rqp

Using the symbolic representations

p: I am an environmentalist.q: I recycle my aluminum

cans.r: I recycle my newspapers.

express the following compound statements in symbolic form.

prq ~)(.3

Using the symbolic representations

p: I am an environmentalist.q: I recycle my aluminum

cans.r: I recycle my newspapers.

express the following compound statements in symbolic form.

pqr ~)~(.4