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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
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उत्तर

Tautology

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अध्याय 1.1: Mathematical Logic - Q.1

संबंधित प्रश्न

Using truth table examine whether the following statement pattern is tautology, contradiction or contingency `(p^^~q) harr (p->q)`


Write the dual of the following statements:

Madhuri has curly hair and brown eyes.


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. 


State if the following sentence is a statement. In case of a statement, write down the truth value :
Every quadratic equation has only real roots.


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


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) ∨ (p ∨ q)] ∧ r ≡ 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) ∧ (p ∧ r)


Prepare truth tables for the following statement pattern.

(~ p ∨ q) ∧ (~ p ∨ ~ q)


Prove that the following statement pattern is a tautology.

(p → q) ↔ (~ q → ~ p)


Show that the following statement pattern is contingency.

(p∧~q) → (~p∧~q)


Show that the following statement pattern is contingency.

p ∧ [(p → ~ q) → q]


Write the dual statement of the following compound statement.

13 is prime number and India is a democratic country.


Write the dual statement of the following compound statement.

Radha and Sushmita cannot read Urdu.


Write the dual statement of the following compound statement.

A number is a real number and the square of the number is non-negative.


Write the negation of the following statement.

∀ n ∈ N, n + 1 > 0


Write the negation of the following statement.

Some continuous functions are differentiable.


Construct the truth table for the following statement pattern.

(p ∨ ~q) → (r ∧ p)


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

[(~p ∧ q) ∧ (q ∧ r)] ∨ (~q)


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

(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)]


Write the dual of the following.

(~p ∧ q) ∨ (p ∧ ~q) ∨ (~p ∧ ~q)


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

Some members of the present Indian cricket are not committed.


The statement pattern (∼ p ∧ q) is logically equivalent to ______.


Write the negation of the following statement:

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


If p → q is true and p ∧ q is false, then the truth value of ∼p ∨ q is ______


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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