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

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प्रश्न

Write the dual of the following.

p ∨ (q ∧ r) ≡ (p ∨ q) ∧ (q ∨ r)

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उत्तर

p ∧ (q ∨ r) ≡ (p ∧ q) ∨ (q ∧ r)

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पाठ 1: Mathematical Logic - Miscellaneous Exercise 1 [पृष्ठ ३३]

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बालभारती Mathematics and Statistics 1 (Commerce) [English] Standard 12 Maharashtra State Board
पाठ 1 Mathematical Logic
Miscellaneous Exercise 1 | Q 4.18 | पृष्ठ ३३

संबंधित प्रश्‍न

Prove that the following statement pattern is equivalent :

(p ∨ q) →  r and (p → r) ∧ (q → r)


Show that the following statement pattern in contingency : 

(~p v q) → [p ∧ (q v ~ q)] 


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


Write the negation of the following statement : 
If the lines are parallel then their slopes are equal.


State if the following sentence is a statement. In case of a statement, write down the truth value :
Every quadratic equation has only real roots.


Using the truth table proves the following logical equivalence.

∼ (p ↔ q) ≡ (p ∧ ∼ q) ∨ (q ∧ ∼ p)


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

(p ∧ q) → (q ∨ p)


(p ∧ q) → r is logically equivalent to ________.


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

[(p ∨ q) ∧ ∼p] ∧ ∼q


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


Prepare truth tables for the following statement pattern.

(p ∧ r) → (p ∨ ~ q)


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

q ∨ [~ (p ∧ q)]


If p is any statement then (p ∨ ∼p) is a ______.


Fill in the blanks :

Inverse of statement pattern p ↔ q is given by –––––––––.


Using the truth table, verify.

p ∨ (q ∧ r) ≡ (p ∨ q) ∧ (p ∨ r)


Using the truth table, verify

p → (p → q) ≡ ~ q → (p → q)


Write the dual of the following:

(p ∨ q) ∨ r


Write the dual of the following:

p ∨ (q ∨ r) ≡ (p ∨ q) ∨ r


Write the dual of the following:

~(p ∧ q) ≡ ~ p ∨ ~ q


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

(~p ∧ q) ∧ (~q ∨ ~r)


Construct the truth table for the following statement pattern.

(~p ∨ q) ∧ (~p ∧ ~q)


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

[(p ∧ q) ∨ (~p)] ∨ [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 ∨ q) ∨ (p ∨ q)] ∧ r ≡ r


Using the truth table, prove the following logical equivalence.

p ↔ q ≡ ~(p ∧ ~q) ∧ ~(q ∧ ~p)


Write the dual of the following.

(p ∧ q) ∧ r ≡ p ∧ (q ∧ r)


Express the truth of the following statement by the Venn diagram.

Some members of the present Indian cricket are not committed.


If p → (∼p v q) is false, then the truth values of p and q are respectively


Write the negation of the following statement:

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


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