Advertisements
Advertisements
Question
Write the dual of the following:
(p ∨ q) ∨ r
Advertisements
Solution
(p ∧ q) ∧ r
APPEARS IN
RELATED QUESTIONS
Examine whether the following logical statement pattern is a tautology, contradiction, or contingency.
[(p→q) ∧ q]→p
Using truth table, examine whether the following statement pattern is tautology, contradiction or contingency: p ∨ [∼(p ∧ q)]
Use the quantifiers to convert the following open sentence defined on N into true statement:
x2 ≥ 1
By constructing the truth table, determine whether the following statement pattern ls a tautology , contradiction or . contingency. (p → q) ∧ (p ∧ ~ q ).
Examine whether the following statement (p ∧ q) ∨ (∼p ∨ ∼q) is a tautology or contradiction or neither of them.
Using the truth table prove the following logical equivalence.
(p ∨ q) → r ≡ (p → r) ∧ (q → 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) ∨ (∼p ∧ q)] ∧ r
Prepare truth tables for the following statement pattern.
p → (~ p ∨ q)
Prepare truth table for (p ˄ q) ˅ ~ r
(p ∧ q) ∨ ~ r
Prove that the following statement pattern is a tautology.
(p → q) ↔ (~ q → ~ p)
Prove that the following statement pattern is a tautology.
(~ p ∨ ~ q) ↔ ~ (p ∧ q)
Prove that the following statement pattern is a contradiction.
(p ∨ q) ∧ (~p ∧ ~q)
If p is any statement then (p ∨ ∼p) is a ______.
Show that the following statement pattern is contingency.
(p → q) ∧ (p → r)
Prove that the following pair of statement pattern is equivalent.
~(p ∧ q) and ~p ∨ ~q
Write the dual statement of the following compound statement.
13 is prime number and India is a democratic country.
Write the converse, inverse, and contrapositive of the following statement.
"If it snows, then they do not drive the car"
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) ∨ (~p)] ∨ [p ∧ (~ q)]
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 ∧ q ≡ [(p ∨ q)] ∧ ~p
Express the truth of the following statement by the Venn diagram.
Some members of the present Indian cricket are not committed.
Show that the following statement pattern is a contingency:
(p→q)∧(p→r)
The converse of contrapositive of ∼p → q is ______.
Examine whether the following statement pattern is a tautology or a contradiction or a contingency.
(p ∧ q) → (q ∨ p)
