मराठी
महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता १२ वी

Using the rule of negation write the negation of the following with justification. (p ∨ ∼ q) ∧ r - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

Using the rule of negation write the negation of the following with justification.

(p ∨ ∼ q) ∧ r

बेरीज

उत्तर

The negation of (p ∨ ∼ q) ∧ r is
∼ [(p ∨ ∼ q) ∧ r] ≡ (p ∨ ∼ q) ∨ ∼ r .........(Negation of conjunction)
≡ [∼ p ∧ ∼ (∼ q)] ∨ ∼ r ......(Negation of disjunction) ≡ (∼ p ∧ q) ∨ ∼ r ...........(Negation of negation)

shaalaa.com
Negations of Compound Statements
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 1: Mathematical Logic - Exercise 1.4 [पृष्ठ २१]

APPEARS IN

संबंधित प्रश्‍न

Write the negation of the following.

3 is not a root of the equation x2 + 3x – 18 = 0


Write the negation of the following.

`sqrt2` is a rational number.


Write the negation of the following.

7 + 3 > 5

Write the negation of the following.

x + 8 > 11 or y – 3 = 6


Write the negation of the following.

11 < 15 and 25 > 20


Write the negation of the following.

Quadrilateral is a square if and only if it is a rhombus.


Write the negation of the following.

If it is raining then we will go and play football.


Write the negation of the following.

All-natural numbers are whole numbers.


Using the rule of negation write the negation of the following with justification.

∼ q → p


Using the rule of negation write the negation of the following with justification.

p ∧ ∼ q


Using the rule of negation write the negation of the following with justification.

p ∨ ∼ q


Using the rule of negation write the negation of the following with justification.

p → (p ∨ ∼ q)


Using the rule of negation write the negation of the following with justification.

∼ (p ∧ q) ∨ (p ∨ ∼ q)


Using the rule of negation write the negation of the following with justification.

(p ∨ ∼ q) → (p ∧ ∼ q)


Select and write the correct answer from the given alternative of the following question:

The negation of inverse of ∼p → q is ________.


The negation of p ∧ (q → r) is ________.


Write the negation of the following:

∀ n ∈ A, n + 7 > 6.


Write the negation of the following:

∃ x ∈ A, such that x + 9 ≤ 15.


The negation of the statement 'He is poor but happy' is ______.


Negation of (∼p → q) is ______.


Negation of (p ∧ q) → (∼p ∨ r) is ______.


The negation of p ^ (q → r) is ______.


The negation of the statement 7 is greater than 4 or 6 is less than 7.


The negation of (p → q) ∧ r is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×