Truth Table, Argument Forms, Morgan Transformation

Question 1

Conjunction - P&Q

Answer 1

Special Case = TTT

The combination of P and Q results in P&Q is true

If there T for P, Q, and P&Q = a T goes there.

Always true when both are true

T
F
F
F

Question 2

Disjunction - P v Q

Answer 2

Special Case = FFF

Opposite of Conjunction

T
T
T
F

Question 3

Exclusive Disjunction - P w Q

Answer 3

Special Case = TTT and FFF

F
T
T
F

Question 4

Conditional – P>Q

Answer 4

Only False when P is True and Q is False
T
F
T
T

Question 5

BiConditional – P#Q

Answer 5

Only All True or All False

T
F
F
T

Question 6

Modus Ponens

Answer 6

Premises -  P >  Q
Premise      P
--------------------------
                              Q
Valid Argument

Question 7

Fools Modus Ponens

Answer 7

Premise - P > Q
Premise - Q
—————————
P

Invalid

Question 8

Modus Tollens

Answer 8

Premise - If P>Q
Premise - ~Q
————————
~P

Valid Argument

Question 9

Fools Modus Tollens

Answer 9

Premise - If P>Q
Premise - ~P
—————————–
~Q

Invalid Argument

Question 10

Hypothetical Syllogism

Answer 10

Premise If P>Q
Premise If Q>R
————————-
P>R

Valid

Question 11

Disjunctive Syllogism

Answer 11

Premise P v Q
Premise ~P
————————
Q

Valid Argument

Question 12

Constructive Dilemma

Answer 12

Premise P v Q
Premise   P>R
Premise   Q>S
-----------------------
                    R or S

Valid

Question 13

Destructive Dilemma

Answer 13

Premise P>R
Premise  Q>S
Premise  ~R or ~S
----------------------------
                          ~P or ~Q

Valid Argument

Question 14

De Morgan Transformation

Answer 14

P>Q = ~(~Pv~Q)

~(P>Q) = (~Pv~Q)

PvQ = (~P&~Q)

~(PvQ) = (~P&~Q)