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प्रश्न
The contrapositive of p → ~ q is ______
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उत्तर
The contrapositive of p → ~ q is q → ~ p
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संबंधित प्रश्न
Using truth table, examine whether the following statement pattern is tautology, contradiction or contingency: p ∨ [∼(p ∧ q)]
Using the truth table prove the following logical equivalence.
(p ∨ q) → r ≡ (p → r) ∧ (q → r)
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 → q)
Determine whether the following statement pattern is a tautology, contradiction or contingency:
(p ∧ q) ∨ (∼p ∧ q) ∨ (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 ∨ q) ∧ (~ p ∨ ~ q)
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
Prove that the following statement pattern is a tautology.
(~ p ∨ ~ q) ↔ ~ (p ∧ q)
Using the truth table, verify
p → (p → q) ≡ ~ q → (p → q)
Using the truth table, verify
~(p → ~q) ≡ p ∧ ~ (~ q) ≡ p ∧ q.
Using the truth table, verify
~(p ∨ q) ∨ (~ p ∧ q) ≡ ~ p
Write the dual of the following:
p ∨ (q ∨ r) ≡ (p ∨ q) ∨ r
Using the rules of negation, write the negation of the following:
(p → r) ∧ q
Using the rules of negation, write the negation of the following:
(~p ∧ q) ∧ (~q ∨ ~r)
Write the converse, inverse, and contrapositive of the following statement.
If he studies, then he will go to college.
With proper justification, state the negation of the following.
(p → q) ∨ (p → r)
Using the truth table, prove the following logical equivalence.
[~(p ∨ q) ∨ (p ∨ q)] ∧ r ≡ r
Using the truth table, prove the following logical equivalence.
p ↔ q ≡ ~(p ∧ ~q) ∧ ~(q ∧ ~p)
The false statement in the following is ______.
Write the converse and contrapositive of the following statements.
“If a function is differentiable then it is continuous”
Write the dual of the following.
13 is prime number and India is a democratic country
Write the negation of the following statement:
(p `rightarrow` q) ∨ (p `rightarrow` r)
If p, q are true statements and r, s are false statements, then find the truth value of ∼ [(p ∧ ∼ r) ∨ (∼ q ∨ s)].
