Principles of Reasoning Exam 2

Question 1

&

Answer 1

and

Question 2

V

Answer 2

or

Question 3

⊃

Answer 3

if….then

Question 4

≡

Answer 4

if and only if

Question 5

~

Answer 5

not

Question 6

P & Q is true when

Answer 6

both P & Q are true (both connectives are true), otherwise it is false

Question 7

P v Q is true when

Answer 7

either P is true, Q is true, or both are true (at least one connective needs to be true)

Question 8

P ⊃ Q is false when

Answer 8

P is true and Q is false (when one connective (T) leads to false)

Question 9

P ≡ Q is true when

Answer 9

P and Q have the same value (both can be true or both can be false)

Question 10

~P is true when

Answer 10

P is false (opposite)

Question 11

Tautologies are always..

Answer 11

TRUE
-P ∨ ~P,
-(P & Q) ⊃ P,
-P ⊃ (P ∨ Q

Question 12

Contradictions are always….

Answer 12

FALSE
-P & ~P
-~(P ∨ ~P)
-P & ~(P ∨ Q

Question 13

Contingencies are sometimes…

Answer 13

TRUE and FALSE
-P & Q
-P ⊃ Q
-P ∨ Q

Question 14

Two propositions are equivalent when…

Answer 14

they have the same truth table
- P and ~~P are equivalent

Question 15

Two propositions are contradictory when….

Answer 15

they have opposite truth tables
- P and ~P are contradictory

Question 16

Two propositions are consistent when…

Answer 16

they are both true on at least one row
-P & Q is consistent with P ˅ Q

Question 17

Valid argument

Answer 17

when a false conclusion has at least one false premise

Question 18

Invalid argument

Answer 18

when there are all true premises and a false conclusion