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

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प्रश्न

Write the dual of the following.

(~p ∧ q) ∨ (p ∧ ~q) ∨ (~p ∧ ~q)

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उत्तर

(~p ∨ q) ∧ (p ∨ ~q) ∧ (~p ∨ ~q)

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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 a tautology : ( q → p ) v ( p → q )


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 ≡ ∼ [(p ∨ q) ∧ ∼ (p ∧ q)]


Using the truth table, prove the following logical equivalence.

p ∧ (q ∨ r) ≡ (p ∧ q) ∨ (p ∧ r)


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

(p ∧ q) → (q ∨ p)


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)


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

∼ (∼ 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 → r)] ↔ [(p ∧ q) → 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)


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)


Write the dual of the following:

~(p ∨ q) ∧ [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)


Construct the truth table for the following statement pattern.

(p ∧ ~ q) ↔ (q → 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


Using the truth table, prove the following logical equivalence.

p ↔ q ≡ ~(p ∧ ~q) ∧ ~(q ∧ ~p)


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

If I do not work hard, then I do not prosper.


Write the dual of the following.

p ∨ (q ∧ r) ≡ (p ∨ q) ∧ (q ∨ r)


Write the dual of the following

(p ˄ ∼q) ˅ (∼p ˄ q) ≡ (p ˅ q) ˄ ∼(p ˄ q)


Choose the correct alternative:

If p → q is an implication, then the implication ~q → ~p is called its


The contrapositive of p → ~ q is ______


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


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


In the triangle PQR, `bar(PQ) = 2bara and bar(QR)` = `2 bar(b)` . The mid-point of PR is M. Find following vectors in terms of `bar(a) and bar(b)` .

  1. `bar(PR)`  
  2. `bar(PM)`
  3. `bar(QM)`

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


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