logic

Question 1

One of the first mathematicians to make a serious study of
symbolic logic (1646 – 1716).
he tried to advance the study of logic from a merely
philosophical subject to a formal mathematical subject.

Answer 1

Gottfried Wilhelm Leibnitz

Question 2

several
mathematicians have contributed to the
advancement of symbolic logic as a mathematical discipline.

Answer 2

Augustus De Morgan (1806 – 1871)
and George Boole (1815 – 1864)

Question 3

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

Answer 3

statements, logical connectives and quantifiers.

Question 4

is a declarative sentence that is either true or false

Answer 4

statement

Question 5

is a statement that conveys a single idea.

Answer 5

simple statement

Question 6

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

Answer 6

compound statement

Question 7

must have the opposite truth value
to the original statement

Answer 7

The negation of a statement

Question 8

~

Answer 8

not

Question 9

^, conjunction

Answer 9

and

Question 10

disjunction, v

Answer 10

or

Question 11

conditional, →

Answer 11

if..then

Question 12

biconditional, ←→

Answer 12

if and only if

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

is 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

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

Answer 17

truth tables

Question 18

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

Answer 18

2n 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

for conditional, p is what??

Answer 22

antecedent

Question 23

for conditional, q is what?

Answer 23

consequent

Question 24

q → p.
if q, then p

Answer 24

converse

Question 25

~p → ~q
if not p, then not q

Answer 25

inverse

Question 26

~q → ~p
if not q, then not p

Answer 26

contrapositive

Question 27

to determine whether logical
arguments are valid or invalid.

Answer 27

deductive reasoning

Question 28

A logical argument is made up of ___ (assumptions,
statements assumed to be true) and a ____

Answer 28

premises and a conclusion

Question 29

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

Answer 29

valid

Question 30

An argument that is not valid

Answer 30

invalid or fallacy