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

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प्रश्न

Write the dual of the following:

~(p ∨ q) ∧ [p ∨ ~ (q ∧ ~ r)]

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उत्तर

~(p ∧ q) ∨ [p ∧ ~ (q ∨ ~ r)]

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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 1.2 | पृष्ठ १७

संबंधित प्रश्‍न

Prove that the following statement pattern is equivalent :

(p ∨ q) →  r and (p → r) ∧ (q → r)


Using truth table examine whether the following statement pattern is tautology, contradiction or contingency `(p^^~q) harr (p->q)`


If   p : It is raining
     q : It is humid

Write the following statements in symbolic form:

(a) It is raining or humid.
(b) If it is raining then it is humid.
(c) It is raining but not humid. 


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 : 
If the lines are parallel then their slopes are equal.


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)


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 ∧ (p → q)] → 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 contradiction.

(p ∨ q) ∧ (~p ∧ ~q)


Show that the following statement pattern is contingency.

(p → q) ∧ (p → r)


Using the truth table, verify

~(p ∨ q) ∨ (~ p ∧ q) ≡ ~ p


Prove that the following pair of statement pattern is equivalent.

p → q and ~ q → ~ p and ~ p ∨ q


Prove that the following pair of statement pattern is equivalent.

~(p ∧ q) and ~p ∨ ~q


Write the dual of the following:

(p ∨ q) ∨ r


Write the dual statement of the following compound statement.

13 is prime number and India is a democratic country.


Write the dual statement of the following compound statement.

Karina is very good or everybody likes her.


With proper justification, state the negation of the following.

(p → q) ∨ (p → r)


With proper justification, state the negation of the following.

(p → q) ∧ r


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)]


Write the converse, inverse, contrapositive of the following statement.

If 2 + 5 = 10, then 4 + 10 = 20.


State the dual of the following statement by applying the principle of duality.

(p ∧ ~q) ∨ (~ p ∧ q) ≡ (p ∨ q) ∧ ~(p ∧ q)


State the dual of the following statement by applying the principle of duality.

p ∨ (q ∨ r) ≡ ~[(p ∧ q) ∨ (r ∨ s)]


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


Write the negation of the following statement:

(p `rightarrow` q) ∨ (p `rightarrow` r)


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


The converse of contrapositive of ∼p → q is ______.


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