Philosophy 251: Handout #6
X. Determine the truth value of each of the following formulas, given that the truth values of the atomic formulas are as follows--P = F, Q = T, R = T.
1. ~[~P v ( ~ Q v ~R )] | 6. ~[ P v ( ~Q & ~R )] |
2. ( P ![]() ![]() |
7. ( P ![]() ![]() ![]() |
3. ( P ![]() ![]() |
8. ~P ![]() ![]() |
4. ~[ R ![]() |
9. ~[~P![]() ![]() ![]() |
5. ~( R ![]() ![]() |
10. ~ [~( P ![]() ![]() ![]() |
XI. Construct complete truth tables for each of the following formulas. For each formula determine whether the formula is contingent, a tautology, or a contradiction.
1. A ![]() ![]() |
6. ( C ![]() ![]() ![]() |
2. ( ~F & ~ G ) v ~( F v G ) | 7. ( D ![]() ![]() ![]() |
3. ~H ![]() ![]() |
8. [( J v K ) & ( J v L )] ![]() |
4. ( M ![]() ![]() |
9. ~[[( P v Q ) & ( Q v R )] & (~P & ~ R)] |
5. ( S v ~T ) ![]() ![]() |
10. [( X v ~Y) & ~( X & Y )] ![]() |
XII. For each of the following
pairs of formulas determine whether imples
,
implies
, or whether
and
are logically equivalent.
|
|
|
|
1. ~( A & B ) | ~( A v B ) | 4. C ![]() ![]() |
( C & ~C ) v ( E ![]() |
2. X ![]() ![]() |
~ ( X ![]() |
5.~( O & P ) ![]() ![]() |
( O & P ) ![]() |
3. ( Q & ~U ) v S | Q v ~ ( ~S & U) |
XIII. For each of the following arguments, construct a truth
table to determine whether the argument is valid or invalid.
1. A ( B & C ),
B
C, ~B / ~A
2. D v ( E & ~ F ), ( F
E )
D, ~D v F
/ ~( E v F )
3. ( G ~H ) & H, (
H v [( I
G ) & I ])
~G / H
~D
4. ~( J K ), ~J, ~K / L
& ~L
5. ( M N )
( N
O ), N / M
O
6. P v P, [ ~P ( ~
Q v ~ R ) ] & [( ~Q v R ) v ( ~P v R )] / R
7. ( S T ) v ( ~S
T ) / (~S
~T
) v ~( S
T )
8. [( U & W ) & X ] v ( ~U
~X ), U
W, W
X / W
X
9. ~~Y ~~Z, ~Z
~Y / Z
Y
10. [A & ( B v C )] (
A v B ), B
~B /
C v A