CR Midterm

Question 1

& is TRUE

only when

Answer 1

Both of them are TRUE

Question 2

v is TRUE when

Answer 2

all the time

except for

when both of them are False, then it is FALSE.

Question 3

⊃ is TRUE when

Answer 3

BOTH of them are TRUE

or

1st FALSE and 2nd TRUE

Question 4

Atomic Proposition

Answer 4

a proposition that doesn’t contain any other proposition as a component

ex: Yuna Kim is famous.

Songdo is in Korea.

Question 5

≡ is true when

Answer 5

BOTH are True

or

BOTH are False

Question 6

An argument is logically valid =def

Answer 6

it is impossible for all of the premises to be true and the conclusion false (in virtue of form and structure).

Question 7

Compound / Complex Proposition

Answer 7

a proposition that is not ATOMIC

ex: Yonsei won 2-2 v Korea University won 2-1.

Question 8

The scope

Answer 8

is the formulas that the connective applies to

in

P v Q

v is connective

P and Q are the scopes.

Question 9

Main connective

Answer 9

the connective that has the widest scope in the formula.

Question 10

Syntax

Answer 10

specifies the grammar of PL (propositional logic)

Question 11

Semantics

Answer 11

give the meaning of ~, &, v, ≡, ⊃

by specifying EXACTLY WHEN they are TRUE.

Question 12

Consistent Statements

Answer 12

there is at least 1 case when both of them are true at the same time

Question 13

Inconsistent Statement

Answer 13

there is NO case when both of them are true at the same time

sometimes contradictory but not always

Question 14

Contradictory Statements

Answer 14

are always INCONSISTENT

F. T

T. F

F. T

Question 15

Logically Equivalent

Answer 15

Mirror image of each other

T. T

F. F

T. T

Not always consistent (when the whole column is F)

Question 16

Tautology

Answer 16

Apply to only one wff (P) 1

(logical truth)

The whole column of the main connective is true

Question 17

Self-contradictory

Answer 17

Applied to a wff

The whole column is FALSE

Question 18

Consistent

Answer 18

applied to a wff

There is at least 1 truth.

Question 19

Contingent

Answer 19

Applied to a wff

There is at least 1 TRUTH and 1 FALSE

Question 21

If the conclusion is a tautology

Answer 21

the argument is always valid

because there is NO counter example (when the premises are T but the conclusion is F)

Question 22

if we have a premise that is self-contradictory

Answer 22

the argument is ALWAYS valid

(there is no counter example)

it can never be SOUND

Question 23

SOUNDNESS

Answer 23

an argument is VALID

and

ALL its PREMISES are TRUE