Question
Download Solution PDFWhich one of the following statements is not a tautology?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFExplanation:
|
p |
q |
~q |
p ∨ ~q |
~p |
p ∧ ~q |
|
T |
T |
F |
T |
F |
F |
|
T |
F |
T |
T |
F |
T |
|
F |
T |
F |
F |
T |
F |
|
F |
F |
T |
T |
T |
F |
|
p |
q |
p ∨ q |
p → p ∨ q |
p ∧ q |
p ∧ q → p |
|
T |
T |
T |
T |
T |
T |
|
T |
F |
T |
T |
F |
T |
|
F |
T |
T |
T |
F |
T |
|
F |
F |
F |
T |
F |
T |
|
p |
q |
~p ∨ q |
(p ∧ q) → (~p) ∨ q |
(p ∨ q) → (p ∨ (~q)) |
|
T |
T |
T |
T |
T |
|
T |
F |
F |
T |
T |
|
F |
T |
T |
T |
F |
|
F |
F |
T |
T |
T |
A tautology is a formula or assertion that is true in every possible interpretation. So, by the truth table (p ∨ q) → (p ∨ (~q)) statement is not a tautology.
A tautology is a statement that is always true, no matter what. If you construct a truth table for a statement and all of the column values for the statement are true (T), then the statement is a tautology because it's always true!
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