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Construct the truth table for the following statement pattern. (p ∨ ~q) → (r ∧ p) - Mathematics and Statistics

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प्रश्न

Construct the truth table for the following statement pattern.

(p ∨ ~q) → (r ∧ p)

योग

उत्तर

p q r ~q p∨~q r∧p (p∨~q)→(r∧p)
T T T F T T T
T T F F T F F
T F T T T T T
T F F T T F F
F T T F F F T
F T F F F F T
F F T T T F F
F F F T T F F
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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 4.11 | पृष्ठ ३३

संबंधित प्रश्न

Prove that the following statement pattern is equivalent :

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( p ∧  ∼ r ) ∧ ( ∼ q ∧ s )


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(c) It is raining but not humid. 


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State if the following sentence is a statement. In case of a statement, write down the truth value :
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Examine whether the following statement (p ∧ q) ∨ (∼p ∨ ∼q) is a tautology or contradiction or neither of them.


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p ↔ q ≡ ∼ [(p ∨ q) ∧ ∼ (p ∧ q)]


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∼ (p ↔ q) ≡ (p ∧ ∼ q) ∨ (q ∧ ∼ p)


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

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

[p → (∼ q ∨ r)] ↔ ∼ [p → (q → r)]


(p ∧ q) → r is logically equivalent to ________.


Prepare truth tables for the following statement pattern.

p → (~ p ∨ q)


Prepare truth tables for the following statement pattern.

(p ∧ r) → (p ∨ ~ q)


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 tautology.

(p → q) ↔ (~ q → ~ p)


Prove that the following statement pattern is a contradiction.

(p ∧ q) ∧ (~p ∨ ~q)


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p → (p → q) ≡ ~ q → (p → q)


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Write the negation of the following statement.

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~(p ∨ q) → r


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(p → q) ∨ (p → 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 ∨ r)] ↔ ~[p → (q → r)]


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

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


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