मराठी
महाराष्ट्र राज्य शिक्षण मंडळएचएससी वाणिज्य (इंग्रजी माध्यम) इयत्ता १२ वी

Write the dual of the following. ~(p ∨ q) ≡ ~p ∧ ~q - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

Write the dual of the following.

~(p ∨ q) ≡ ~p ∧ ~q

एका वाक्यात उत्तर

उत्तर

~(p ∧ q) ≡ ~p ∨ ~q

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 1: Mathematical Logic - Miscellaneous Exercise 1 [पृष्ठ ३३]

APPEARS IN

बालभारती Mathematics and Statistics 1 (Commerce) [English] 12 Standard HSC Maharashtra State Board
पाठ 1 Mathematical Logic
Miscellaneous Exercise 1 | Q 4.18 | पृष्ठ ३३

संबंधित प्रश्‍न

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


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 )


Using truth table, examine whether the following statement pattern is tautology, contradiction or contingency: p ∨ [∼(p ∧ q)]


Show that the following statement pattern in contingency : 

(~p v q) → [p ∧ (q v ~ q)] 


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


State if the following sentence is a statement. In case of a statement, write down the truth value :
√-4 is a rational number.


Using the truth table prove the following logical equivalence.

p ↔ q ≡ ∼ [(p ∨ q) ∧ ∼ (p ∧ q)]


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) ↔ (∼ p ∨ q)


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

∼ (∼ q ∧ p) ∧ q


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

(∼ p → q) ∧ (p ∧ r)


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


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

[(p ∨ q) ∧ ∼p] ∧ ∼q


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

(p → q) ∨ (q → p)


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

q ∨ [~ (p ∧ q)]


Prove that the following statement pattern is a tautology.

(p → q) ↔ (~ q → ~ p)


Prove that the following statement pattern is a contradiction.

(p ∧ q) ∧ ~p


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


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)


Write the dual of the following:

(p ∨ q) ∨ r


Write the dual of the following:

~(p ∨ q) ∧ [p ∨ ~ (q ∧ ~ r)]


Write the dual statement of the following compound statement.

13 is prime number and India is a democratic country.


Write the negation of the following statement.

Some continuous functions are differentiable.


With proper justification, state the negation of the following.

(p → q) ∧ r


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)


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) → p] ↔ [(~p) ∧ (~q)]


Write the dual of the following

(p ˄ ∼q) ˅ (∼p ˄ q) ≡ (p ˅ q) ˄ ∼(p ˄ q)


Choose the correct alternative:

If p → q is an implication, then the implication ~q → ~p is called its


If p → (∼p v q) is false, then the truth values of p and q are respectively


Which of the following is not equivalent to p → q.


Show that the following statement pattern is a contingency:

(p→q)∧(p→r)


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

(∼p ∧ ∼q) → (p → q)


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×