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

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प्रश्न

Write the dual of the following:

(p ∨ q) ∨ r

एक पंक्ति में उत्तर

उत्तर

(p ∧ q) ∧ r

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अध्याय 1: Mathematical Logic - Exercise 1.7 [पृष्ठ १७]

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बालभारती Mathematics and Statistics 1 (Commerce) [English] 12 Standard HSC Maharashtra State Board
अध्याय 1 Mathematical Logic
Exercise 1.7 | Q 1.1 | पृष्ठ १७

संबंधित प्रश्न

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

[(p→q) ∧ q]→p


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 )


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


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 ≡ ∼ [(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 ∨ q) ∨ (p ∨ q)] ∧ r ≡ r


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) ↔ (p → q)


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

(∼ p → q) ∧ (p ∧ 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 → (q → r)] ↔ [(p ∧ q) → r]


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) ∨ (q → p)


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)


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

~ p → (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∧~q)


Show that the following statement pattern is contingency.

(p → q) ↔ (~ p ∨ q)


Prove that the following pair of statement pattern is equivalent.

p ↔ q and (p → q) ∧ (q → p)


Prove that the following pair of statement pattern is equivalent.

~(p ∧ q) and ~p ∨ ~q


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 → 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 ∧ r) → (p ∨ ~q)


Construct the truth table for the following statement pattern.

(p ∨ ~q) → (r ∧ p)


What is tautology? What is contradiction?
Show that the negation of a tautology is a contradiction and the negation of a contradiction is a tautology.


Using the truth table, prove the following logical equivalence.

p ↔ q ≡ ~(p ∧ ~q) ∧ ~(q ∧ ~p)


Using the truth table, prove the following logical equivalence.

~p ∧ q ≡ [(p ∨ q)] ∧ ~p


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

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


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

Some members of the present Indian cricket are not committed.


Choose the correct alternative:

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


Complete the truth table.

p q r q → r r → p (q → r) ˅ (r → p)
T T T T `square` T
T T F F `square` `square`
T F T T `square` T
T F F T `square` `square`
F T T `square` F T
F T F `square` T `square`
F F T `square` F T
F F F `square` T `square`

The given statement pattern is a `square`


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


Which of the following is not true for any two statements p and q?


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)`

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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