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

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प्रश्न

Write the dual of the following.

~(p ∨ q) ≡ ~p ∧ ~q

एक पंक्ति में उत्तर

उत्तर

~(p ∧ q) ≡ ~p ∨ ~q

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अध्याय 1: Mathematical Logic - Miscellaneous Exercise 1 [पृष्ठ ३३]

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बालभारती Mathematics and Statistics 1 (Commerce) [English] 12 Standard HSC Maharashtra State Board
अध्याय 1 Mathematical Logic
Miscellaneous Exercise 1 | Q 4.18 | पृष्ठ ३३

संबंधित प्रश्न

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

[(p→q) ∧ q]→p


Write the converse and contrapositive of the statement -
“If two triangles are congruent, then their areas are equal.”


Express the following statement in symbolic form and write its truth value.

"If 4 is an odd number, then 6 is divisible by 3 "


Write the dual of the following statements:

Madhuri has curly hair and brown eyes.


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


Express the following statement in symbolic form and write its truth value.
"If 4 is an odd number, then 6 is divisible by 3."


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


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


Using the truth table prove the following logical equivalence.

(p ∨ q) → r ≡ (p → r) ∧ (q → r)


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 ∨ r) ≡ (p ∧ q) ∨ (p ∧ r)


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) ∧ ∼ q] → ∼ p


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

[p → (∼ q ∨ r)] ↔ ∼ [p → (q → r)]


Inverse of statement pattern (p ∨ q) → (p ∧ q) is ________ .


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 ∧ ~q)


Prove that the following statement pattern is a contradiction.

(p ∧ q) ∧ ~p


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 (p → q) ∧ (q → p)


Prove that the following pair of statement pattern is equivalent.

p → q and ~ q → ~ p and ~ p ∨ q


Write the dual of the following:

(p ∨ q) ∨ r


Write the negation of the following statement.

Some continuous functions are differentiable.


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)


Construct the truth table for the following statement pattern.

(p ∨ r) → ~(q ∧ r)


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)


State the dual of the following statement by applying the principle of duality.

p ∨ (q ∨ r) ≡ ~[(p ∧ q) ∨ (r ∨ s)]


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

Some members of the present Indian cricket are not committed.


Write the dual of the following

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


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


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


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