SENTENTIAL LOGIC
USING TRUTH TABLES TO SHOW RELATIONSHIP BETWEEN
SENTENCES: IMPLICATION (which direction) or EQUIVALENCE
LOGICAL IMPLICATION
One sentence logically implies the second if the truth of the first
guarantees the truth of the second.
TO SHOW LOGICAL IMPLICATION
1. Make the truth table of both sentences, side by side.
2. Read the truth table.
Does (1) imply (2)? Check from (1) to (2) whether there is never T F
Does (2) imply (1)? Check from (2) to (1) whether there is never T F
Sentence 1
~(A V B)
F
Sentence 2
~(A & B)
F
A
T
B
T
AVB
T
A&B
T
T
F
T
F
F
F
F
T
T
F
F
F
F
F
F
F
T
T
TRUTH FUNCTIONAL EQUIVALENCE
Two sentences (containing the same letters) are truth functionally
equivalent if their truth values are identical for each possible truth value
assignment of the atomic claims. That is, two sentences are truth
functionally equivalent if they have identical truth values on each possible
row of their truth table.
~A V B
AB
A
B
~A
T
T
F
T
T
T
F
F
F
F
F
T
T
T
T
F
F
T
T
T