Memorize for Midterm

Question 1

How do you construct a truth table?

Answer 1

1. List component in increasing complexity
2. Determine the amount of rows by 2 ^ # of atomic sentences
3. Alternate truth table values, by 4, then 2, then within the rows

Question 2

The Law of Double Negation (example and abbreviation)

Answer 2

DN. ~~x = x

Question 3

De Morgan’s Law (ex. and ab.)

Answer 3

DM. 1. ~(X&Y) = ~Xv~Y
2. ~(XvY) = ~X&~Y
NOTICE THE SWITCH FROM CONJUNCTION TO DISJUNCTION, and vice versa

Question 4

The Distributive Law (ex. and ab.)

Answer 4

D. For any 3 sentences, X,Y, and Z, X&(YvZ) = (X&Y)v(X&Z)
Pay attention to the connectives!!

Question 5

The Law of Transitivity (ex. and ab.)

Answer 5

TLE. If X=Y and Y=Z, then X=Z.

Question 6

Communicative Law (ex. and ab.)

Answer 6

CM. X&Y=Y&X
Disjuncts and conjuncts.

Question 7

Associative Law (ex. and ab.)

Answer 7

A. X&(Y&Z)=(X&Y)&Z

Question 8

Law of Redundancy (ex. and ab.)

Answer 8

RD. X&X=X

Question 9

Logical Truth Example

Answer 9

Mv~M

Question 10

Contradiction Example

Answer 10

M&~M

Question 11

Law of Logically True Conjunct (ex. and ab.)

Answer 11

LTC. X is any sentence and Y is a LT, then X&Y = X

Question 12

Law of Contradictory Disjunct (ex. and ab.)

Answer 12

LCD. X is any sentence and Y is ant C, then XvY = X

Question 13

A conjunction is always a contradiction when…

Answer 13

one of its conjuncts is a contradiction.

Question 14

A disjunction is always a logical truth when…

Answer 14

one of its disjuncts in a logical truth.

Question 15

How to determine Disjunctive Normal Form

Answer 15

1. Draw the truth table
2. In every case (row), put conjunction between every true column.
3. Put disjuncts between the newly created compounds with conjuncts.

Question 16

Define Expressive Completeness

Answer 16

When a connective, or set of them can represent every truth function.
Disjunction, conjunction, and negation, taken together, are Expressively Complete.

Question 17

How to determine validity from a truth table

Answer 17

1. Look when the conclusion is true
2. In those places, if every premise is true, circle it
3. If there are any counterexamples, or those rows where the conclusion is true but not ALL the premises are, then invalid argument
4. If it’s made it this far, it’s valid

Question 18

Law of Contraposition (ex. and ab.)

Answer 18

CP. X->Y = ~Y->~X

Question 19

Law of the Conditional (ex. and ab.)

Answer 19

C. X->Y = ~(X&Y) and (~XvY)

Question 20

Law of the BiConditional (ex. and ab.)

Answer 20

B. A biconditional is the same as (X->Y)&(Y->X)

Question 21

Explain Modus Tollens (denying the consequent) give abbreviation

Answer 21

DC. Assume the antecedent and show the contradiction to arrive at the conclusion

Question 22

Explain Reductio Ad Adsurdum (ab.)

Answer 22

RD. From X, arriving at Y&~Y, then X is actually ~X

Question 23

Explain Argument by Cases. (ab.)

Answer 23

AC. If a disjunction, and the disjuncts both have the same consequent in a conditional, you prove the consequent as true.
Still must show the mini-proof!