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

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प्रश्न

Write the dual of the following.

p ∨ (q ∧ r) ≡ (p ∨ q) ∧ (q ∨ r)

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उत्तर

p ∧ (q ∨ r) ≡ (p ∧ q) ∨ (q ∧ r)

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

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

संबंधित प्रश्न

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 )


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)]


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


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 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.

∼ (∼ q ∧ p) ∧ q


Prepare truth tables for the following statement pattern.

p → (~ p ∨ q)


Prepare truth tables for the following statement pattern.

(~ p ∨ q) ∧ (~ p ∨ ~ q)


Prepare truth tables for the following statement pattern.

(p ∧ r) → (p ∨ ~ q)


Prove that the following statement pattern is a tautology.

(p ∧ q) → q


Prove that the following statement pattern is a contradiction.

(p ∧ q) ∧ ~p


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


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)


Write the dual of the following:

~(p ∨ q) ∧ [p ∨ ~ (q ∧ ~ r)]


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

(p → r) ∧ q


With proper justification, state the negation of the following.

(p → q) ∨ (p → r)


Construct the truth table for the following statement pattern.

(p ∧ r) → (p ∨ ~q)


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 ∨ r)] ↔ ~[p → (q → r)]


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

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


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

p ∨ (q ∨ r) ≡ ~[(p ∧ q) ∨ (r ∨ s)]


Choose the correct alternative:

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


Using truth table verify that:

(p ∧ q)∨ ∼ q ≡ p∨ ∼ q


Write the negation of the following statement:

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


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


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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