English

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

Advertisements
Advertisements

Question

Write the dual of the following.

(~p ∧ q) ∨ (p ∧ ~q) ∨ (~p ∧ ~q)

One Line Answer
Advertisements

Solution

(~p ∨ q) ∧ (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] Standard 12 Maharashtra State Board
Chapter 1 Mathematical Logic
Miscellaneous Exercise 1 | Q 4.18 | Page 33

RELATED QUESTIONS

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

[(p→q) ∧ q]→p


Prove that the following statement pattern is equivalent :

(p ∨ q) →  r and (p → r) ∧ (q → r)


Write the dual of the following statements:

Madhuri has curly hair and brown eyes.


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 )


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 → r) ∧ (q → r)


Using the truth table prove the following logical equivalence.

p → (q ∧ r) ≡ (p → q) ∧ (p → r)


Using the truth table proves the following logical equivalence.

∼ (p ↔ q) ≡ (p ∧ ∼ q) ∨ (q ∧ ∼ p)


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 ∨ r)] ↔ ∼ [p → (q → r)]


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


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 contradiction.

(p ∧ q) ∧ (~p ∨ ~q)


Show that the following statement pattern is contingency.

(p → q) ↔ (~ p ∨ q)


Prove that the following pair of statement pattern is equivalent.

~(p ∧ q) and ~p ∨ ~q


Write the negation of the following statement.

All the stars are shining if it is night.


Write the negation of the following statement.

Some continuous functions are differentiable.


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)] ∧ r ≡ 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) ∨ (~ 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)]


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

Some members of the present Indian cricket are not committed.


Write the converse and contrapositive of the following statements.

“If a function is differentiable then it is continuous”


Write the dual of the following

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


The contrapositive of p → ~ q is ______


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


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

(∼p ∧ ∼q) → (p → q)


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×