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

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प्रश्न

Write the dual of the following:

p ∨ (q ∨ r) ≡ (p ∨ q) ∨ r

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उत्तर

p ∧ (q ∧ r) ≡ (p ∧ q) ∧ r

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  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
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 1.3 | पृष्ठ १७

संबंधित प्रश्‍न

Write the dual of the following statements:

Madhuri has curly hair and brown eyes.


Write the negation of the Following Statement :
∀ y ∈  N, y2 + 3 ≤ 7


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 ∧ q) ≡ ∼ p


Using the truth table, prove the following logical equivalence.

p ∧ (q ∨ r) ≡ (p ∧ q) ∨ (p ∧ r)


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

[(p ∧ (p → q)] → q


Prepare truth tables for the following statement pattern.

p → (~ p ∨ q)


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.

(~ q ∧ p) ∧ (p ∧ ~ 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


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)


Write the dual of the following:

(p ∨ q) ∨ r


Write the dual of the following:

~(p ∨ q) ∧ [p ∨ ~ (q ∧ ~ r)]


Write the dual statement of the following compound statement.

13 is prime number and India is a democratic country.


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) v (~ q → ~ r)


Construct the truth table for the following statement pattern.

(p ∨ ~q) → (r ∧ p)


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)] ∧ r ≡ r


The statement pattern (p ∧ q) ∧ [~ r v (p ∧ q)] v (~ p ∧ q) is equivalent to ______. 


The equivalent form of the statement ~(p → ~ q) is ______.


The statement pattern (∼ p ∧ q) is logically equivalent to ______.


Show that the following statement pattern is a contingency:

(p→q)∧(p→r)


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

(∼p ∧ ∼q) → (p → q)


If p → q is true and p ∧ q is false, then the truth value 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)].


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