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Choose the correct alternative: If p is any statement, then (p ˅ ~p) is a - Mathematics and Statistics

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प्रश्न

Choose the correct alternative:

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

विकल्प

  • Contingency

  • Contradiction

  • Tautology

  • None of these

MCQ

उत्तर

Tautology

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अध्याय 1.1: Mathematical Logic - Q.1

संबंधित प्रश्न

Write the converse and contrapositive of the statement -
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Express the following statement in symbolic form and write its truth value.

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Show that the following statement pattern in contingency : 

(~p v q) → [p ∧ (q v ~ q)] 


Write converse and inverse of the following statement :
"If Ravi is good in logic then Ravi is good in Mathematics."


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) ↔ (∼ 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.

(p ∧ ∼ q) ↔ (p → q)


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


Prepare truth tables for the following statement pattern.

(~ p ∨ q) ∧ (~ p ∨ ~ q)


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

(~ q ∧ p) ∧ (p ∧ ~ p)


Prove that the following statement pattern is a contradiction.

(p ∧ q) ∧ ~p


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)


Using the truth table, verify

p → (p → q) ≡ ~ q → (p → q)


Prove that the following pair of statement pattern is equivalent.

~(p ∧ q) and ~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 of the following:

~(p ∧ q) ≡ ~ p ∨ ~ q


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∃ n ∈ N, (n2 + 2) is odd number.


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"If it snows, then they do not drive the car"


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If he studies, then he will go to college.


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(p ∧ ~ q) ↔ (q → p)


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(~p ∨ q) ∧ (~p ∧ ~q)


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

[~(p ∧ q) → p] ↔ [(~p) ∧ (~q)]


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[p → (~q ∨ r)] ↔ ~[p → (q → r)]


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[~(p ∨ q) ∨ (p ∨ q)] ∧ r ≡ r


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p ↔ q ≡ ~(p ∧ ~q) ∧ ~(q ∧ ~p)


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If a man is bachelor, then he is happy.


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(p ∧ ~q) ∨ (~ p ∧ q) ≡ (p ∨ q) ∧ ~(p ∧ q)


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

p ∨ (q ∨ r) ≡ ~[(p ∧ q) ∨ (r ∨ s)]


The contrapositive of p → ~ q is ______


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


Using truth table verify that:

(p ∧ q)∨ ∼ 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.

(p ∧ q) → (q ∨ p)


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