हिंदी

State the dual of the following statement by applying the principle of duality. 2 is even number or 9 is a perfect square. - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

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

2 is even number or 9 is a perfect square.

एक पंक्ति में उत्तर

उत्तर

2 is even number and 9 is a perfect square.

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 1: Mathematical Logic - Miscellaneous Exercise 1 [पृष्ठ ३३]

APPEARS IN

बालभारती Mathematics and Statistics 1 (Commerce) [English] 12 Standard HSC Maharashtra State Board
अध्याय 1 Mathematical Logic
Miscellaneous Exercise 1 | Q 4.16 | पृष्ठ ३३

संबंधित प्रश्न

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

[(p→q) ∧ q]→p


Write the dual of the following statements:

Madhuri has curly hair and brown eyes.


Use the quantifiers to convert the following open sentence defined on N into true statement
5x - 3 < 10


Write the negation of the Following Statement :
∀ y ∈  N, y2 + 3 ≤ 7


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 ∧ r) ≡ (p → q) ∧ (p → 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


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


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

[p → (q → r)] ↔ [(p ∧ q) → r]


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

(p → q) ∨ (q → p)


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)


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 contradiction.

(p → q) ∧ (p ∧ ~ q)


Show that the following statement pattern is contingency.

(p → q) ∧ (p → r)


Write the dual of the following:

~(p ∧ q) ≡ ~ p ∨ ~ 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.

Karina is very good or everybody likes her.


Write the negation of the following statement.

∃ n ∈ N, (n2 + 2) is odd number.


Using the rules of negation, write the negation of the following:

(p → r) ∧ q


With proper justification, state the negation of the following.

(p → q) ∨ (p → r)


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

[(p ∧ q) ∨ (~p)] ∨ [p ∧ (~ q)]


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

[(~p ∧ q) ∧ (q ∧ r)] ∨ (~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 dual of the following.

(p ∧ q) ∧ r ≡ p ∧ (q ∧ r)


The false statement in the following is ______.


Write the dual of the following.

13 is prime number and India is a democratic country


The statement pattern (p ∧ q) ∧ [~ r v (p ∧ q)] v (~ p ∧ q) is equivalent to ______. 


The equivalent form of the statement ~(p → ~ q) is ______.


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


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)`

If p, q are true statements and r, s are false statements, then find the truth value of ∼ [(p ∧ ∼ r) ∨ (∼ q ∨ s)].


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×