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

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प्रश्न

Write the dual of the following:

p ∨ (q ∨ r) ≡ (p ∨ q) ∨ r

एक पंक्ति में उत्तर

उत्तर

p ∧ (q ∧ r) ≡ (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 1.3 | पृष्ठ १७

संबंधित प्रश्न

Write converse and inverse of the following statement: 
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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) ↔ (∼ p ∨ q)


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, 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 ∧ [(p → ~ q) → q]


Using the truth table, verify.

p ∨ (q ∧ r) ≡ (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 (p → q) ∧ (q → p)


Prove that the following pair of statement pattern is equivalent.

~(p ∧ q) and ~p ∨ ~q


Write the dual of the following:

~(p ∧ q) ≡ ~ p ∨ ~ q


Write the negation of the following statement.

∃ n ∈ N, (n2 + 2) is odd number.


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

~(p ∨ q) → r


With proper justification, state the negation of the following.

(p ↔ q) v (~ q → ~ r)


Construct the truth table for the following statement pattern.

(p ∧ ~ q) ↔ (q → p)


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 ∨ r) ≡ (p ∧ q) ∨ (p ∧ r)


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 a man is bachelor, then he is happy.


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

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


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

Some members of the present Indian cricket are not committed.


Write the converse and contrapositive of the following statements.

“If a function is differentiable then it is continuous”


Choose the correct alternative:

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


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


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


Write the negation of the following statement:

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


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

(∼p ∧ ∼q) → (p → q)


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)`

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