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महाराष्ट्र राज्य शिक्षण मंडळएचएससी वाणिज्य (इंग्रजी माध्यम) इयत्ता १२ वी

If p is any statement then (p ∨ ∼p) is a ______. - Mathematics and Statistics

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प्रश्न

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

पर्याय

  • Contingency

  • Contradiction

  • Tautology

  • None of them

MCQ
रिकाम्या जागा भरा

उत्तर

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

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पाठ 1: Mathematical Logic - Miscellaneous Exercise 1 [पृष्ठ ३०]

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बालभारती Mathematics and Statistics 1 (Commerce) [English] 12 Standard HSC Maharashtra State Board
पाठ 1 Mathematical Logic
Miscellaneous Exercise 1 | Q 1.15 | पृष्ठ ३०

संबंधित प्रश्‍न

Prove that the following statement pattern is equivalent :

(p ∨ q) →  r and (p → r) ∧ (q → r)


Write the dual of the following statements:

Madhuri has curly hair and brown eyes.


Write converse and inverse of the following statement: 
“If a man is a bachelor then he is unhappy.” 


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


If p and q are true statements and r and s are false statements, find the truth value of the following :
( p ∧  ∼ r ) ∧ ( ∼ q ∧ s )


Prove that the following statement pattern is equivalent:
(p v q) → r and (p → r) ∧ (q → r)


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


State if the following sentence is a statement. In case of a statement, write down the truth value :
√-4 is a rational number.


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) ∨ (p ∨ q)] ∧ r ≡ r


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

[p → (∼ q ∨ r)] ↔ ∼ [p → (q → r)]


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 ∧ (p → q)] → q


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

[(p ∨ ∼q) ∨ (∼p ∧ q)] ∧ r


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

(~ q ∧ p) ∧ (p ∧ ~ p)


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 tautology.

(p ∧ q) → q


Fill in the blanks :

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


Show that the following statement pattern is contingency.

(p∧~q) → (~p∧~q)


Show that the following statement pattern is contingency.

p ∧ [(p → ~ q) → 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 dual statement of the following compound statement.

A number is a real number and the square of the number is non-negative.


Write the negation of the following statement.

All the stars are shining if it is night.


With proper justification, state the negation of the following.

(p ↔ q) v (~ q → ~ r)


With proper justification, state the negation of the following.

(p → q) ∧ r


Construct the truth table for the following statement pattern.

(~p ∨ q) ∧ (~p ∧ ~q)


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 ∧ (~p ∨ q) ≡ p ∧ q


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) ≡ ~p ∧ ~q


Choose the correct alternative:

If p is any statement, then (p ˅ ~p) is a


The contrapositive of p → ~ q is ______


Which of the following is not equivalent to p → q.


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


Using truth table verify that:

(p ∧ q)∨ ∼ q ≡ p∨ ∼ q


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

[(∼ p ∧ q) ∧ (q ∧ r)] ∧ (∼ q)


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) → (q ∨ p)


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