# logic Flashcards

1
Q

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.

A

Gottfried Wilhelm Leibnitz

2
Q

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

A

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

3
Q

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

A

statements, logical connectives and quantifiers.

4
Q

is a declarative sentence that is either true or false

A

statement

5
Q

is a statement that conveys a single idea.

A

simple statement

6
Q

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

A

compound statement

7
Q

must have the opposite truth value
to the original statement

A

The negation of a statement

8
Q

~

A

not

9
Q

^, conjunction

A

and

10
Q

disjunction, v

A

or

11
Q

conditional, →

A

if..then

12
Q

biconditional, ←→

A

if and only if

13
Q

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.

A

truth value

14
Q

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

A

truth table

15
Q

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

A

Universal quantifier

16
Q

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

A

Existential quantifier

17
Q

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

A

truth tables

18
Q

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

A

2n rows

19
Q

is a statement that is always true.

A

tautology

20
Q

is a statement that is always false.

A

21
Q

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

A

equivalent

22
Q

for conditional, p is what??

A

antecedent

23
Q

for conditional, q is what?

A

consequent

24
Q

q → p.
if q, then p

A

converse

25
Q

~p → ~q
if not p, then not q

A

inverse

26
Q

~q → ~p
if not q, then not p

A

contrapositive

27
Q

to determine whether logical
arguments are valid or invalid.

A

deductive reasoning

28
Q

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

A

premises and a conclusion

29
Q

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

A

valid

30
Q

An argument that is not valid

A

invalid or fallacy