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Write the dual of the following: ~(p ∧ q) ≡ ~ p ∨ ~ q - Mathematics and Statistics

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प्रश्न

Write the dual of the following:

~(p ∧ q) ≡ ~ p ∨ ~ q

एका वाक्यात उत्तर
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उत्तर

~(p ∨ q) ≡ ~ p ∧ ~ q

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पाठ 1: Mathematical Logic - Exercise 1.7 [पृष्ठ १७]

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बालभारती Mathematics and Statistics 1 (Commerce) [English] Standard 12 Maharashtra State Board
पाठ 1 Mathematical Logic
Exercise 1.7 | Q 1.4 | पृष्ठ १७

संबंधित प्रश्‍न

Write the dual of the following statements: (p ∨ q) ∧ T


Prove that the following statement pattern is a tautology : ( q → p ) v ( p → q )


Use the quantifiers to convert the following open sentence defined on N into true statement:
x2 ≥ 1


Write converse and inverse of the following statement :
"If Ravi is good in logic then Ravi is good in Mathematics."


Using the truth table prove the following logical equivalence.

p → (q → p) ≡ ∼ 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)


Determine whether the following statement pattern is a tautology, contradiction, or contingency:

[(p ∨ q) ∧ ∼p] ∧ ∼q


Prepare truth tables for the following statement pattern.

(p ∧ r) → (p ∨ ~ q)


Prove that the following pair of statement pattern is equivalent.

p → q and ~ q → ~ p and ~ p ∨ q


Write the dual statement of the following compound statement.

13 is prime number and India is a democratic country.


Write the negation of the following statement.

Some continuous functions are differentiable.


Using the rules of negation, write the negation of the following:

~(p ∨ q) → r


With proper justification, state the negation of the following.

(p → q) ∨ (p → r)


Construct the truth table for the following statement pattern.

(~p ∨ q) ∧ (~p ∧ ~q)


Construct the truth table for the following statement pattern.

(p ∧ r) → (p ∨ ~q)


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 ∧ (~p ∨ q) ≡ p ∧ q


Write the dual of the following.

(p ∧ q) ∧ r ≡ p ∧ (q ∧ r)


Write the dual of the following.

p ∨ (q ∧ r) ≡ (p ∨ q) ∧ (q ∨ r)


Write the dual of the following.

~(p ∨ q) ≡ ~p ∧ ~q


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.


Show that the following statement pattern is a contingency:

(p→q)∧(p→r)


If p → q is true and p ∧ q is false, then the truth value of ∼p ∨ q is ______


Prepare truth table for the statement pattern `(p -> q) ∨ (q -> p)` and show that it is a tautology.


If p, q are true statements and r, s are false statements, then find the truth value of ∼ [(p ∧ ∼ r) ∨ (∼ q ∨ s)].


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