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Using the rules of negation, write the negation of the following: ~(p ∨ q) → r - Mathematics and Statistics

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प्रश्न

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

~(p ∨ q) → r

योग
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उत्तर

~[~ (p ∨ q) → r] ≡ ~ (p ∨ q) ∧ ~ r      ...[Negation of implication]

≡ (~ p ∧ ~ q) ∧ ~ r        ...[De-morgan's law]

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अध्याय 1: Mathematical Logic - Exercise 1.8 [पृष्ठ २१]

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बालभारती Mathematics and Statistics 1 (Commerce) [English] Standard 12 Maharashtra State Board
अध्याय 1 Mathematical Logic
Exercise 1.8 | Q 2.2 | पृष्ठ २१

संबंधित प्रश्न

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

[(p→q) ∧ q]→p


Prove that the following statement pattern is equivalent :

(p ∨ q) →  r and (p → r) ∧ (q → r)


If   p : It is raining
     q : It is humid

Write the following statements in symbolic form:

(a) It is raining or humid.
(b) If it is raining then it is humid.
(c) It is raining but not humid. 


Using truth table, examine whether the following statement pattern is tautology, contradiction or contingency: p ∨ [∼(p ∧ q)]


Use the quantifiers to convert the following open sentence defined on N into true statement
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Every quadratic equation has only real roots.


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)] ∧ r


Prepare truth tables for the following statement pattern.

(~ p ∨ q) ∧ (~ p ∨ ~ q)


Prove that the following statement pattern is a tautology.

(~p ∧ ~q ) → (p → q)


Prove that the following statement pattern is a contradiction.

(p ∧ q) ∧ ~p


Show that the following statement pattern is contingency.

(p → 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 statement of the following compound statement.

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


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

If he studies, then he will go to college.


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 ∧ (~p ∨ q) ≡ p ∧ q


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


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p ∨ (q ∨ r) ≡ ~[(p ∧ q) ∨ (r ∨ s)]


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


Write the negation of the following statement:

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


The converse of contrapositive of ∼p → q is ______.


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