Advertisements
Advertisements
Question
Determine whether the following statement pattern is a tautology, contradiction or contingency:
[(p ∨ ∼q) ∨ (∼p ∧ q)] ∧ r
Advertisements
Solution
| p | q | r | ∼p | ∼q | p ∨ ∼q | ∼p ∧ q | (p ∨ ∼q) ∨ (∼p ∧ q) | (I) ∧ r |
| (I) | ||||||||
| T | T | T | F | F | T | F | T | T |
| T | T | F | F | F | T | F | T | F |
| T | F | T | F | T | T | F | T | T |
| T | F | F | F | T | T | F | T | F |
| F | T | T | T | F | F | T | T | T |
| F | T | F | T | F | F | T | T | F |
| F | F | T | T | T | T | F | T | T |
| F | F | F | T | T | T | F | T | F |
The entries in the last column are neither all T nor all F.
∴ [(p ∨ ∼q) ∨ (∼p ∧ q)] ∧ r is a contingency.
APPEARS IN
RELATED QUESTIONS
Using truth table, examine whether the following statement pattern is tautology, contradiction or contingency: p ∨ [∼(p ∧ q)]
Show that the following statement pattern in contingency :
(~p v q) → [p ∧ (q v ~ q)]
Prove that the following statement pattern is equivalent:
(p v q) → r and (p → r) ∧ (q → r)
State if the following sentence is a statement. In case of a statement, write down the truth value :
Every quadratic equation has only real roots.
By constructing the truth table, determine whether the following statement pattern ls a tautology , contradiction or . contingency. (p → q) ∧ (p ∧ ~ q ).
Using the truth table prove the following logical equivalence.
(p ∨ q) → r ≡ (p → r) ∧ (q → r)
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 → (q ∧ r) ≡ (p ∧ q) (p → r)
Using the truth table proves the following logical equivalence.
∼ (p ↔ q) ≡ (p ∧ ∼ q) ∨ (q ∧ ∼ p)
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 ∨ q)
Examine whether the following statement pattern is a tautology or a contradiction or a contingency.
(∼ p → q) ∧ (p ∧ r)
Determine whether the following statement pattern is a tautology, contradiction, or contingency:
[(p ∨ q) ∧ ∼p] ∧ ∼q
Determine whether the following statement pattern is a tautology, contradiction or contingency:
[p → (q → r)] ↔ [(p ∧ q) → r]
Prepare truth tables for the following statement pattern.
p → (~ p ∨ q)
Examine whether the following statement pattern is a tautology, a contradiction or a contingency.
q ∨ [~ (p ∧ q)]
Prove that the following statement pattern is a tautology.
(p → q) ↔ (~ q → ~ p)
Prove that the following statement pattern is a contradiction.
(p ∧ q) ∧ ~p
If p is any statement then (p ∨ ∼p) is a ______.
Prove that the following statement pattern is a contradiction.
(p ∧ q) ∧ (~p ∨ ~q)
Prove that the following statement pattern is a contradiction.
(p → q) ∧ (p ∧ ~ q)
Show that the following statement pattern is contingency.
(p → q) ↔ (~ p ∨ q)
Show that the following statement pattern is contingency.
(p → q) ∧ (p → r)
Using the truth table, verify
~(p → ~q) ≡ p ∧ ~ (~ q) ≡ p ∧ q.
Using the truth table, verify
~(p ∨ q) ∨ (~ p ∧ q) ≡ ~ p
Prove that the following pair of statement pattern is equivalent.
p ↔ q and (p → q) ∧ (q → p)
Prove that the following pair of statement pattern is equivalent.
p → q and ~ q → ~ p and ~ p ∨ q
Prove that the following pair of statement pattern is equivalent.
~(p ∧ q) and ~p ∨ ~q
Using the rules of negation, write the negation of the following:
~(p ∨ q) → r
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 ∨ r) → ~(q ∧ r)
Construct the truth table for the following statement pattern.
(p ∨ ~q) → (r ∧ p)
Determine whether the following statement pattern is a tautology, contradiction, or contingency.
[(~p ∧ q) ∧ (q ∧ r)] ∨ (~q)
Determine whether the following statement pattern is a tautology, contradiction, or contingency.
[~(p ∨ q) → p] ↔ [(~p) ∧ (~q)]
Determine whether the following statement pattern is a tautology, contradiction, or contingency.
[~(p ∧ q) → p] ↔ [(~p) ∧ (~q)]
Write the dual of the following.
(p ∧ q) ∧ r ≡ p ∧ (q ∧ r)
Express the truth of the following statement by the Venn diagram.
Some members of the present Indian cricket are not committed.
The false statement in the following is ______.
Choose the correct alternative:
If p → q is an implication, then the implication ~q → ~p is called its
The statement pattern (p ∧ q) ∧ [~ r v (p ∧ q)] v (~ p ∧ q) is equivalent to ______.
Which of the following is not equivalent to p → q.
Write the negation of the following statement:
(p `rightarrow` q) ∨ (p `rightarrow` r)
The converse of contrapositive of ∼p → q is ______.
If p, q are true statements and r, s are false statements, then find the truth value of ∼ [(p ∧ ∼ r) ∨ (∼ q ∨ s)].
