English

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

Advertisements
Advertisements

Question

Write the dual of the following.

~(p ∨ q) ≡ ~p ∧ ~q

One Line Answer

Solution

~(p ∧ q) ≡ ~p ∨ ~q

shaalaa.com
  Is there an error in this question or solution?
Chapter 1: Mathematical Logic - Miscellaneous Exercise 1 [Page 33]

APPEARS IN

Balbharati Mathematics and Statistics 1 (Commerce) [English] 12 Standard HSC Maharashtra State Board
Chapter 1 Mathematical Logic
Miscellaneous Exercise 1 | Q 4.18 | Page 33

RELATED QUESTIONS

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 : 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. 


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


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


By constructing the truth table, determine whether the following statement pattern ls a tautology , contradiction or . contingency.  (p →  q) ∧  (p ∧ ~ q ).


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) ≡ ∼ p → (p → q)


Using the truth table prove the following logical equivalence.

p ∧ (q ∨ r) ≡ (p ∧ q) ∨ (p ∧ 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


(p ∧ q) → r is logically equivalent to ________.


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

(p → q) ∨ (q → p)


Prove that the following statement pattern is a contradiction.

(p ∨ q) ∧ (~p ∧ ~q)


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)


Using the truth table, verify

p → (p → q) ≡ ~ q → (p → q)


Write the dual statement of the following compound statement.

Karina is very good or everybody likes her.


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.

∃ n ∈ N, (n2 + 2) is odd number.


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

(p → r) ∧ q


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

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


Construct the truth table for the following statement pattern.

(p ∧ ~ q) ↔ (q → p)


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) ∨ (~p)] ∨ [p ∧ (~ q)]


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 ∨ r)] ↔ ~[p → (q → r)]


Using the truth table, prove the following logical equivalence.

p ↔ q ≡ ~(p ∧ ~q) ∧ ~(q ∧ ~p)


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)


Write the dual of the following.

p ∨ (q ∧ r) ≡ (p ∨ q) ∧ (q ∨ r)


The false statement in the following is ______.


Write the dual of the following

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


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

(p ∧ q) → (q ∨ p)


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×