हिंदी

If p is any statement then (p ∨ ∼p) is a ______. - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

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

विकल्प

  • Contingency

  • Contradiction

  • Tautology

  • None of them

MCQ
रिक्त स्थान भरें

उत्तर

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

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 1: Mathematical Logic - Miscellaneous Exercise 1 [पृष्ठ ३०]

APPEARS IN

बालभारती Mathematics and Statistics 1 (Commerce) [English] 12 Standard HSC Maharashtra State Board
अध्याय 1 Mathematical Logic
Miscellaneous Exercise 1 | Q 1.15 | पृष्ठ ३०

संबंधित प्रश्न

Express the following statement in symbolic form and write its truth value.

"If 4 is an odd number, then 6 is divisible by 3 "


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 )


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 (p ∧ q) ∨ (∼p ∨ ∼q) is a tautology or contradiction or neither of them.


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 ∨ r)] ↔ ∼ [p → (q → r)]


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


Prepare truth tables for the following statement pattern.

p → (~ p ∨ q)


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

(p ∧ ~ q) → (~ p ∧ ~ q)


Prove that the following statement pattern is a tautology.

(p ∧ q) → q


Prove that the following statement pattern is a tautology.

(~ 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 ∧ [(p → ~ q) → q]


Using the truth table, verify

~(p → ~q) ≡ p ∧ ~ (~ q) ≡ p ∧ q


Using the truth table, verify

~(p ∨ q) ∨ (~ p ∧ q) ≡ ~ p


Write the dual of the following:

p ∨ (q ∨ r) ≡ (p ∨ q) ∨ r


Write the dual statement of the following compound statement.

Karina is very good or everybody likes her.


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)


Construct the truth table for the following statement pattern.

(p ∨ ~q) → (r ∧ p)


What is tautology? What is contradiction?
Show that the negation of a tautology is a contradiction and the negation of a contradiction is a tautology.


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

[(~p ∧ q) ∧ (q ∧ r)] ∨ (~q)


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

[~(p ∨ q) → p] ↔ [(~p) ∧ (~q)]


Using the truth table, prove the following logical equivalence.

~p ∧ q ≡ [(p ∨ q)] ∧ ~p


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

If a man is bachelor, then he is happy.


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

If I do not work hard, then I do not prosper.


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

2 is even number or 9 is a perfect square.


Write the dual of the following.

(~p ∧ q) ∨ (p ∧ ~q) ∨ (~p ∧ ~q)


Write the dual of the following.

(p ∧ q) ∧ r ≡ p ∧ (q ∧ r)


Write the dual of the following.

~(p ∨ q) ≡ ~p ∧ ~q


The false statement in the following is ______.


Write the dual of the following.

13 is prime number and India is a democratic country


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

(∼p ∧ ∼q) → (p → q)


In the triangle PQR, `bar(PQ) = 2bara and bar(QR)` = `2 bar(b)` . The mid-point of PR is M. Find following vectors in terms of `bar(a) and bar(b)` .

  1. `bar(PR)`  
  2. `bar(PM)`
  3. `bar(QM)`

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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×