Chapter 3 Terms

Question 1

Logic

Answer 1

• The science of correct reasoning

- Used within many professions (law, computer programmers, engineers, authors, etc.)

Question 2

Statement

Answer 2

• A declarative sentence that is either true or false but not both true and false
• You do not have to know for sure that it is true or false, you just know that it must be

Question 3

Simple Statement

Answer 3

• A statement that conveys a single idea

- It can be true or false

Question 4

Compound Statement

Answer 4

• A statement that conveys two or more ideas
• Connects simple statements with words and phrases (and, or, if … then, if and only if)
• Truth value depends upon the true or false of each statement and how the statements are connected

Question 5

p

Answer 5

Connective: –
Symbolic form: p
Statement type: simple

Question 6

not p

Answer 6

Connective: ~
Symbolic form: ~p
Statement type: negation

Question 7

p and q

Answer 7

Connective: and
Symbolic form: p( upward arrow )q
Statement type: conjunction

Question 8

p or q

Answer 8

Connective: or
Symbolic form: p( downward arrow )q
Statement type: disjunction

Question 9

If p, then q`

Answer 9

Connective: if… ,then
Symbolic form: p -> q
Statement type: conditional

Question 10

p if and only if q

Answer 10

Connective: if and only if
Symbolic form: p q
Statement type: bi-conditional

Question 11

What do you know once you know that something is a statement?

Answer 11

• You know that statement is either true or false

Question 12

Quantifier

Answer 12

• Describes an amount
• Universal
• All, every, none, no

Question 13

Negation

Answer 13

• Taking a statement and making it false or true
• All x are y = Some x are not y
• No x are y = Some x are y
• Some x are y = No x are y
• Some x are not y = All x are y

Question 14

Truth Table

Answer 14

• Shows the truth value of a compound statement for all possible truth values of its simple statements

Question 15

Tautology

Answer 15

• A logic statement that is always true

- To express something by saying it or repeating it in a different way

Question 16

Self-Contradiction

Answer 16

• A statement that is always false

Question 17

Conditional Statements

Answer 17

• If… then
• First term is the antecedent
• Second term is the consequent

Question 18

Converse Statement

Answer 18

• A conditional statement that has been reversed

- q -> p

Question 19

Inverse Statement

Answer 19

• A conditional statement that has been negated

- ~p -> ~q

Question 20

Contrapositive Statement

Answer 20

• A conditional statement that has been reversed and negated

- ~q -> ~p

Question 21

Interesting Stuff

Answer 21

• Conditional = Contrapositive

- Converse = inverse

Question 22

Argument

Answer 22

• A set of statements that includes premises and a conclusion

Question 23

Valid Argument

Answer 23

• If the conclusion is true whenever all premises are true

Question 24

Invalid Argument

Answer 24

• An argument that is not a valid argument

Question 25

Syllogism

Answer 25

• An argument as a series of statements (premises) logically progressing to a final statement (conclusion)

Question 26

How to write an argument

Answer 26

• Premise
• Premise
• Conclusion

Question 27

Determine the Validity of an Argument

Answer 27

• Write the argument in symbolic form
• Construct a truth table
• Check for validity