Chapter 5 - Logic

Question 1

One of the first mathematicians to make a serious study of symbolic logic was?

Answer 1

Gottfried Wilhelm Leibnitz

Question 2

He tried to advance the study of logic from a merely philosophical subject to a formal mathematical subject.

Answer 2

Gottfried Wilhelm Leibnitz

Question 3

Leibnitz tried to advance the study of logic from a merely philosophical subject to a formal mathematical subject. Leibnitz never completely achieved this goal; however, several mathematicians, such as? contributed to the advancement of symbolic logic as a mathematical discipline.

Answer 3

Augustus De Morgan and George Boole

Question 4

Logic main goal?

Answer 4

use logic to analyze arguments (claims) to see if they are valid or invalid.

Question 5

To analyze an argument, we break it down into smaller pieces:

Answer 5

statements, logical connectives and quantifiers

Question 6

Every language contains different types of sentences, such as statements, questions, and commands.

Answer 6

Logic Statement

Question 7

Every language contains different types of sentences, such as?

Answer 7

statements, questions, and commands

Question 8

The symbolic logic that Boole was instrumental in creating applies only to sentences that are?

Answer 8

statements

Question 9

is a declarative sentence that is either true or false (but not both at the same time)

Answer 9

statement

Question 10

is a statement that conveys a single idea.

Answer 10

simple statement

Question 11

consists of simple statements combined using logical connectives like and, or, not, if…..then.

Answer 11

compound statement

Question 12

statement must have the opposite truth value to the original statement

Answer 12

negation

Question 13

• a simple statement is either true (T) or false (F).
• a compound statement depends on the truth values of its simple statements and its connectives.

Answer 13

truth value

Question 14

a table that shows the truth value of a compound statement for all possible truth values of its simple statements.

Answer 14

truth table

Question 15

all, every, each. Statement is true if the claim is true for every object it is referring to.

Answer 15

Universal quantifier

Question 16

some, there exists, for at least one.
Statement is true if the claim is true for atleast one object it is referring to.

Answer 16

Existential quantifier

Question 17

a compound statement for all possible truth values of the component statements

Answer 17

truth value

Question 18

If there are n component statements, then the truth table has

Answer 18

2^n rows

Question 19

is a statement that is always true.

Answer 19

tautology

Question 20

is a statement that is always false.

Answer 20

self-contradiction

Question 21

Two statements are? if they have the same truth value for every possible situation, and we write p = q

Answer 21

equivalent

Question 22

will use? to determine whether logical arguments are valid or invalid.

Answer 22

deductive reasoning

Question 23

A logical argument is made up of?

Answer 23

premises and conclusion

Question 24

An argument is? if the fact that all the premises are true forces the conclusion to be true.

Answer 24

valid

Question 25

An argument that is not valid is?

Answer 25

invalid, or a fallacy

Question 26

The three dots are a symbol for?

Answer 26

therefore