Advertisements
Advertisements
Question
State the dual of the following statement by applying the principle of duality.
(p ∧ ~q) ∨ (~ p ∧ q) ≡ (p ∨ q) ∧ ~(p ∧ q)
Solution
(p ∨ ~q) ∧ (~ p ∨ q) ≡ (p ∧ q) ∨ ~(p ∨ q)
APPEARS IN
RELATED QUESTIONS
Write the converse and contrapositive of the statement -
“If two triangles are congruent, then their areas are equal.”
Write the dual of the following statements: (p ∨ q) ∧ T
Using truth table, examine whether the following statement pattern is tautology, contradiction or contingency: p ∨ [∼(p ∧ q)]
Express the following statement in symbolic form and write its truth value.
"If 4 is an odd number, then 6 is divisible by 3."
Use the quantifiers to convert the following open sentence defined on N into true statement
5x - 3 < 10
Write the negation of the Following Statement :
∀ y ∈ N, y2 + 3 ≤ 7
Write the negation of the following statement :
If the lines are parallel then their slopes are equal.
Examine whether the following statement pattern is a tautology or a contradiction or a contingency.
[(p → q) ∧ ∼ q] → ∼ p
Determine whether the following statement pattern is a tautology, contradiction or contingency:
[(p ∨ ∼q) ∨ (∼p ∧ q)] ∧ r
Examine whether the following statement pattern is a tautology, a contradiction or a contingency.
(p ∧ ~ 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)
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 → (p → q) ≡ ~ q → (p → q)
Write the dual statement of the following compound statement.
Karina is very good or everybody likes her.
Write the dual statement of the following compound statement.
A number is a real number and the square of the number is non-negative.
Using the rules of negation, write the negation of the following:
(~p ∧ q) ∧ (~q ∨ ~r)
With proper justification, state the negation of the following.
(p → q) ∧ r
Construct the truth table for the following statement pattern.
(p ∨ r) → ~(q ∧ r)
Determine whether the following statement pattern is a tautology, contradiction, or contingency.
[~(p ∧ q) → p] ↔ [(~p) ∧ (~q)]
Using the truth table, prove the following logical equivalence.
~p ∧ q ≡ [(p ∨ q)] ∧ ~p
Write the converse, inverse, contrapositive of the following statement.
If a man is bachelor, then he is happy.
Write the dual of the following.
p ∨ (q ∧ r) ≡ (p ∨ q) ∧ (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 ______.
Write the dual of the following
(p ˄ ∼q) ˅ (∼p ˄ q) ≡ (p ˅ q) ˄ ∼(p ˄ q)
Write the dual of the following.
13 is prime number and India is a democratic country
Examine whether the statement pattern
[p → (~ q ˅ r)] ↔ ~[p → (q → r)] is a tautology, contradiction or contingency.
If p → (∼p v q) is false, then the truth values of p and q are respectively
Which of the following is not true for any two statements p and q?
Examine whether the following statement pattern is a tautology or a contradiction or a contingency.
(p ∧ q) → (q ∨ p)