Advertisements
Advertisements
Question
Show that the following statement pattern is contingency.
(p → q) ↔ (~ p ∨ q)
Advertisements
Solution
| p | q | ~p | p→q | ~p∨q | (p→q)↔(~p∨q) |
| T | T | F | T | T | T |
| T | F | F | F | F | T |
| F | T | T | T | T | T |
| F | F | T | T | T | T |
All the truth values in the last column are T. Hence, it is a tautology. Not contingency.
APPEARS IN
RELATED QUESTIONS
Examine whether the following logical statement pattern is a tautology, contradiction, or contingency.
[(p→q) ∧ q]→p
Write the dual of the following statements: (p ∨ q) ∧ T
Use the quantifiers to convert the following open sentence defined on N into true statement:
x2 ≥ 1
Using the truth table prove the following logical equivalence.
p → (q ∧ r) ≡ (p → q) ∧ (p → r)
Examine whether the following statement pattern is a tautology or a contradiction or a contingency.
(p ∧ q) → (q ∨ p)
Examine whether the following statement pattern is a tautology or a contradiction or a contingency.
(∼ p → q) ∧ (p ∧ r)
Examine whether the following statement pattern is a tautology or a contradiction or a contingency.
[p → (∼ q ∨ r)] ↔ ∼ [p → (q → r)]
Determine whether the following statement pattern is a tautology, contradiction or contingency:
[p → (q → r)] ↔ [(p ∧ q) → r]
Determine whether the following statement pattern is a tautology, contradiction or contingency:
[(p ∧ (p → q)] → q
Prepare truth tables for the following statement pattern.
p → (~ p ∨ q)
Fill in the blanks :
Inverse of statement pattern p ↔ q is given by –––––––––.
Using the truth table, verify
~(p → ~q) ≡ p ∧ ~ (~ q) ≡ p ∧ q.
Prove that the following pair of statement pattern is equivalent.
p ↔ q and (p → q) ∧ (q → p)
Write the negation of the following statement.
All the stars are shining if it is night.
Write the negation of the following statement.
∀ n ∈ N, n + 1 > 0
Using the rules of negation, write the negation of the following:
(~p ∧ q) ∧ (~q ∨ ~r)
Construct the truth table for the following statement pattern.
(p ∧ ~ q) ↔ (q → p)
What is tautology? What is contradiction?
Show that the negation of a tautology is a contradiction and the negation of a contradiction is a tautology.
Determine whether the following statement pattern is a tautology, contradiction, or contingency.
[(~p ∧ q) ∧ (q ∧ r)] ∨ (~q)
Using the truth table, prove the following logical equivalence.
p ∧ (q ∨ r) ≡ (p ∧ q) ∨ (p ∧ r)
Using the truth table, prove the following logical equivalence.
p ∧ (~p ∨ q) ≡ p ∧ q
Using the truth table, prove the following logical equivalence.
p ↔ q ≡ ~(p ∧ ~q) ∧ ~(q ∧ ~p)
Write the converse, inverse, contrapositive of the following statement.
If a man is bachelor, then he is happy.
The false statement in the following is ______.
If p → q is true and p ∧ q is false, then the truth value of ∼p ∨ q is ______
The converse of contrapositive of ∼p → q is ______.
