हिंदी

Write the dual of the following: ~(p ∨ q) ∧ [p ∨ ~ (q ∧ ~ r)] - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

Write the dual of the following:

~(p ∨ q) ∧ [p ∨ ~ (q ∧ ~ r)]

एक पंक्ति में उत्तर

उत्तर

~(p ∧ q) ∨ [p ∧ ~ (q ∨ ~ r)]

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 1: Mathematical Logic - Exercise 1.7 [पृष्ठ १७]

APPEARS IN

बालभारती Mathematics and Statistics 1 (Commerce) [English] 12 Standard HSC Maharashtra State Board
अध्याय 1 Mathematical Logic
Exercise 1.7 | Q 1.2 | पृष्ठ १७

संबंधित प्रश्न

Write the converse and contrapositive of the statement -
“If two triangles are congruent, then their areas are equal.”


Write the dual of the following statements:

Madhuri has curly hair and brown eyes.


Prove that the following statement pattern is a tautology : ( q → p ) v ( p → q )


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. 


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


Express the following statement in symbolic form and write its truth value.
"If 4 is an odd number, then 6 is divisible by 3."


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


Using the truth table prove the following logical equivalence.

∼ (p ∨ q) ∨ (∼ p ∧ q) ≡ ∼ p


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.

(p ∧ ∼ q) ↔ (p → q)


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)] ∧ r


Prepare truth tables for the following statement pattern.

(~ p ∨ q) ∧ (~ 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 contradiction.

(p ∧ q) ∧ (~p ∨ ~q)


Prove that the following statement pattern is a contradiction.

(p → q) ∧ (p ∧ ~ q)


Using the truth table, verify

~(p → ~q) ≡ p ∧ ~ (~ q) ≡ p ∧ q


Write the dual of the following:

(p ∨ q) ∨ r


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) v (~ q → ~ r)


With proper justification, state the negation of the following.

(p → q) ∧ r


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

[~(p ∨ q) → p] ↔ [(~p) ∧ (~q)]


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

If 2 + 5 = 10, then 4 + 10 = 20.


Write the dual of the following.

p ∨ (q ∧ r) ≡ (p ∨ q) ∧ (q ∨ r)


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

Some members of the present Indian cricket are not committed.


The false statement in the following is ______.


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)


Using truth table verify that:

(p ∧ q)∨ ∼ q ≡ p∨ ∼ q


Write the negation of the following statement:

(p `rightarrow` q) ∨ (p `rightarrow` 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.

(p ∧ q) → (q ∨ p)


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×