Logic Strand Lecture 3

Example:
• Use the “quick” method for the statement
~ ( P ∨ Q)
∧ P to determine if it is a contradiction.
~ (P ∨ Q) ∧ P
Step: 2 1 3*
1.Place “T” under main
connective
T
2. For “T” to occur
under the main
connective, ~ must be
“T” and P must be “T”
T
T
3. For “T” to occur
under ~,
“F”.
P ∨ Q must be
F
4. For “F” to occur
under P ∨ Q, P must be
“F” and Q must be “F”
F
F
P cannot be both “T” and “F”, thus ~ ( P ∨ Q)
∧ P can only
ever be false and is a contradiction.
WUCT121 Logic 46