PRACTICE for CATEGORICAL PROPOSITIONS
For each statement, symbolize it as an A E I or O statement. For example, using c
for cats and a for amphibians, No cats are amphibians will be symbolized as Eca.
1. Every flute is an instrument.
2. At least one music
PRACTICE for REPLACEMENT RULES
Using the implication rules and the first five replacement rules (Association, Commutation,
Distribution, De Morgans, & Double Negation), complete the following proofs. Scroll for answers.
1. ~ R
2. ~ ( P Q )
3. ~ R P
PRACTICE for TRUTH TABLES
There are four sections of exercises.
Section 1: Provided that X and Y are false, and Z is true, determine the truth value of
the following statements. Scroll for answers.
1. [ ~ ( X V Y ) Z ]
2. ~cfw_ [ ( X Y) Z ] V ( X Z )
PRACTICE for SYLLOGISMS
For the following syllogisms (i) translate each sentence into A, E, I, O form and
(ii) determine whether it is valid or invalid.
1. There exists a cat who is precocious.
Every cat is bossy.
It is not the case that no bossy things a
MORE PRACTICE for TRUTH TABLES
What is the relationship between the following statements?
1. ( C V D ) ( ~ C V D )
2. ( J K ) ( ~ J V K )
3. ( ~ A B ) ( ~ B V A )
4. [ ( P ~ R ) Q ] [ Q ( P R) ]
5. ( ~ R S ) ( ~ S R )
6. ~ ( E F ) ( E ~ F )
7. ( X Y ) ( Y
PRACTICE for LOGICAL OPERATORS
*There are three sections of problems*
Section 1: Are the following expressions well-formed formulas or not? Scroll down for answers.
1. [ ~( P V Q ) R ]
2. ~cfw_ [ ( R Y) S ] V ( P T )
3. [ ( ~ P ) ( R S ) ]
4. ( P ~ S )
MORE PRACTICE for IMPLICATION RULES
Section 1: Using only the eight implication rules, complete the following proofs. Scroll down for answers.
1. [ A V ( B A ) ]
2. ~ A C
:. ~ B
1. ( D V E ) ( F G )
1. ( A V B ) ~ C
PRACTICE for ABSORPTION
Section 1: Complete the following proofs using the eight implication rules from the
book, as well as absorption. Scroll down for answers.
1. A B
2. ( A B ) C
:. A C
1. ~ ( K L )
2. K L
:. ~ K
1. [ D ( D A ) ] ( B C )
DUE: MONDAY JUNE 15TH
HOMEWORK 10: EXTENDED PROOFS
Using the eight implication rules, and only the first five replacement rules (DN, DM, Assoc, Com,
Dist), complete the following proofs. (30 points)
1. P ( ~ P V ~ Q )
2. Q V P
3. Q S
4. ~ ( P Q ) R
HOMEWORK 7: CATEGORICAL PROPOSITIONS
DUE: FRIDAY JUNE 6TH
For each of the following syllogisms (i) symbolize each sentence as an A, E, I, or O
statement, (ii) complete the Venn diagram by labeling each circle and shading or placing an
x where appropriate,
HOMEWORK 9: TRUTH TABLES & PROOFS
DUE: FRIDAY JUNE 12TH
Construct a formal proof for each of the following. Remember to include the rule you are using and the
appropriate line numbers for justification. (20 points)
1. (Q V P) (~Q P)
HOMEWORK 8: TRUTH TABLES
DUE: TUESDAY JUNE 9TH
If W and X are both true, Y and Z are both false, then what is the truth value of the
following statements? (2 points each)
1. cfw_ [ X ( Y W ) ] Z
2. [ ( W Y ) ~( Z X ) ]
3. cfw_ Z [ ( W Y ) ( ~ X Z ) ]
PRACTICE for IMPLICATION RULES
Using only the eight implication rules, complete the following proofs. Scroll down for answers.
:. ( A V C ) B
1. ( G H ) ( I J )
:. ( H V J )
1. ( D E )
2. ( D F )
1. ( M N ) ( M O )