English

Write the negation of the following. 11 < 15 and 25 > 20 - Mathematics and Statistics

Advertisements
Advertisements

Question

Write the negation of the following.

11 < 15 and 25 > 20

Sum

Solution

Let p: 11 < 15, q: 25 > 20

Then the symbolic form of the given statement is p ∧ q.

Since ∼ (p ∧ q) ≡ ∼ p ∨ ∼ q, the negation of the given statement is:

11 ≥ 15 or 25 ≤ 20.

shaalaa.com
Negations of Compound Statements
  Is there an error in this question or solution?
Chapter 1: Mathematical Logic - Exercise 1.3 [Page 18]

RELATED QUESTIONS

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.

Polygon ABCDE is a pentagon.


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.

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


Write the negation of the following.

It is cold and raining.


Write the negation of the following.

All-natural numbers are whole numbers.


Write the negation of the following.

∀ n ∈ N, n2 + n + 2 is divisible by 4.


Write the negation of the following.

∃ x ∈ N such that x – 17 < 20


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)


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:

∃ x ∈ A, such that x + 9 ≤ 15.


Write the negation of the following:

Some triangles are equilateral triangle.


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


The negation of the statement pattern ~ p v(q → ~ r) is ______.


Negation of the statement 'A is rich but silly' is ______


Negation of (∼p → q) is ______.


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


The negation of the statement, ∃ x ∈ R, such that x3 + 8 > 0, is ______.


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×