मराठी
महाराष्ट्र राज्य शिक्षण मंडळएचएससी वाणिज्य (इंग्रजी माध्यम) इयत्ता १२ वी

Write the negation of the statement “An angle is a right angle if and only if it is of measure 90°”

Advertisements
Advertisements

प्रश्न

Write the negation of the statement “An angle is a right angle if and only if it is of measure 90°”

बेरीज
Advertisements

उत्तर

Let p: An angle is a right angle.

q: An angle is of measure 90°

The given statement is p ↔ q

Its negation is ~(p ↔ q) ≡ (p ∧ ~q) ∨ (q ∧ ~p)

∴ The negation of given statement is ‘An angle is a right angle and it is not of measure 90° or an angle is of measure 90° and it is not a right angle.’

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 1.1: Mathematical Logic - Q.4

व्हिडिओ ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्‍न

Write down the following statements in symbolic form :

(A) A triangle is equilateral if and only if it is equiangular.
(B) Price increases and demand falls


Using truth table prove that ∼p ˄ q ≡ (p ˅ q) ˄ ∼p


Using truth table, prove that ~ p ∧ q ≡ (p ∨ q) ∧ ~ p


Write the following compound statement symbolically.

x is not irrational number but is a square of an integer.


Construct the truth table of the following statement pattern.

[(p → q) ∧ q] → p


Express the following statement in symbolic form.

Even though it is cloudy, it is still raining.


Write the negation of the following statement.

2 + 3 ≠ 5


Find the truth value of the following statement.

It is not true that 3 − 7i is a real number.


If p and q are true and r and s are false, find the truth value of the following compound statement.

[(p ∨ s) → r] ∨ ~ [~ (p → q) ∨ s]


Assuming that the following statement is true,

p : Sunday is holiday,

q : Ram does not study on holiday,

find the truth values of the following statements.

Sunday is not holiday or Ram studies on holiday.


Assuming that the following statement is true,

p : Sunday is holiday,

q : Ram does not study on holiday,

find the truth values of the following statements.

Sunday is a holiday and Ram studies on holiday.


If p : He swims

q : Water is warm

Give the verbal statement for the following symbolic statement:

p ↔ ~ q


If p : He swims

q : Water is warm

Give the verbal statement for the following symbolic statement.

q ∧ ~ p


State whether the following statement is True or False:

The negation of 10 + 20 = 30 is, it is false that 10 + 20 ≠ 30.


Assuming the first statement p and second as q. Write the following statement in symbolic form.

Kavita is brilliant and brave.


Assuming the first statement p and second as q. Write the following statement in symbolic form.

If Kiran drives the car, then Sameer will walk.


Assuming the first statement p and second as q. Write the following statement in symbolic form.

If the question paper is not easy then we shall not pass.


Write the negation of the following.

Kanchanganga is in India and Everest is in Nepal.


Write the negation of the following.

If x ∈ A ∩ B, then x ∈ A and x ∈ B.


Negation of p → (p ˅ ∼ q) is ______


Negation of “Some men are animal” is ______.


If c denotes the contradiction then the dual of the compound statement ∼p ∧ (q ∨ c) is ______ 


Which of the following is false?


The inverse of the statement "If its quality is good. then it is expensive.", is ______ 


The Boolean expression ∼(p ∨ q) ∨ (∼p ∧ q) is equivalent to ______ 


The negation of the statement: "Getting above 95% marks is a necessary condition for Hema to get admission in good college'' is ______


The logical statement (∼p → q) ∧ (q → p) is equivalent to: ______ 


Write the following statement in symbolic form.

It is not true that `sqrt(2)` is a rational number.


Write the contrapositive of the inverse of the statement:

‘If two numbers are not equal, then their squares are not equal’.


Let p: I am brave.
      q: I will climb the Mount Everest.

The symbolic form of a statement,

‘I am neither brave nor I will climb the mount Everest’ is


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×