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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)

बेरीज

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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पाठ 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
पाठ 1 Mathematical Logic
Miscellaneous Exercise 1 | Q 4.11 | पृष्ठ ३३

संबंधित प्रश्‍न

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√-4 is a rational number.


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

(p ∧ q) → (q ∨ p)


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

[(p ∨ q) ∧ ∼p] ∧ ∼q


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[p → (q → r)] ↔ [(p ∧ q) → r]


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(p ∧ r) → (p ∨ ~ q)


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(p ∧ ~ q) → (~ p ∧ ~ q)


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(p → q) ↔ (~ q → ~ p)


Prove that the following statement pattern is a tautology.

(~ p ∨ ~ q) ↔ ~ (p ∧ q)


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Prove that the following statement pattern is a contradiction.

(p ∧ q) ∧ (~p ∨ ~q)


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All the stars are shining if it is night.


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~(p ∨ q) → r


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(p ∧ ~ q) ↔ (q → p)


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(~p ∨ q) ∧ (~p ∧ ~q)


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[~(p ∨ q) ∨ (p ∨ q)] ∧ r ≡ r


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Using truth table verify that:

(p ∧ q)∨ ∼ q ≡ p∨ ∼ q


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