मराठी
महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) 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 symbolic form of the above Statement is p ↔ q.

∼ (p ↔ q) ≅ (p ∧ ∼ q) ∨ (q ∧ ∼p).

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

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 1.1: Mathematical Logic - Long Answers II

व्हिडिओ ट्यूटोरियलVIEW ALL [3]

संबंधित प्रश्‍न

Examine whether each of the following statement patterns is a tautology or a contradiction or a contingency.

[~(~p ∧ ~q)] v q


Write the following compound statement symbolically.

Nagpur is in Maharashtra and Chennai is in Tamil Nadu. 


Write the following compound statement symbolically.

The angle is right angle if and only if it is of measure 90°.


Write the following compound statement symbolically.

Angle is neither acute nor obtuse.


Write the following compound statement symbolically.

If ΔABC is right-angled at B, then m∠A + m∠C = 90°.


Write the following compound statement symbolically. 

Hima Das wins gold medal if and only if she runs fast.


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:

[(p ∧ q) ∨ r] ∧ [∼r ∨ (p ∧ q)]


Construct the truth table of the following:

[(∼p ∨ q) ∧ (q → r)] → (p → r)


Express the following statement in symbolic form.

e is a vowel or 2 + 3 = 5


Write the truth value of the following statement.

Earth is a planet and Moon is a star.


Write the following statement in symbolic form.

If triangle is equilateral then it is equiangular.


Write the following statement in symbolic form.

Milk is white if and only if the sky is not blue.


Find the truth value of the following statement.

Neither 27 is a prime number nor divisible by 4.


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.

If Sunday is not holiday then Ram studies on holiday.


Fill in the blanks :

Conjunction of two statement p and q is symbolically written as ______.


Negation of “some men are animal” is ______.


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.

Even though it is not cloudy, it is still raining.


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

It is not true that intelligent persons are neither polite nor helpful.


Write the negation of the following.

Ramesh is intelligent and he is hard working.


Write the negation of the following.

If x ∈ A ∩ B, then x ∈ A and x ∈ B.


Assuming the following statement.

p : Stock prices are high.

q : Stocks are rising.

to be true, find the truth value of the following.

Stock prices are high or stocks are not rising iff stocks are rising.


Rewrite the following statement without using the connective ‘If ... then’.

If 10 − 3 = 7 then 10 × 3 ≠ 30.


Rewrite the following statement without using the connective ‘If ... then’.

If it rains then the principal declares a holiday.


A biconditional statement is the conjunction of two ______ statements.


Write the following compound statements symbolically.

Triangle is equilateral or isosceles


Without using truth table prove that:

~ (p ∨ q) ∨ (~ p ∧ q) ≡ ~ p


Write the following statement in symbolic form:

Milk is white if and only if the sky is not blue.


Write the following statements in symbolic form

If Kutab – Minar is in Delhi then Taj - Mahal is in Agra


State whether the following statement is True or False:

The converse of inverse of ~ p → q is q → ~ p


If p : Every natural number is a real number.
q : Every integer is a complex number. Then truth values of p → q and p ↔ q are ______ and ______ respectively.


Which of the following is false?


The negation of (p ∨ ∼q) ∧ q is ______


The negation of ∼s ∨ (∼r ∧ s) is equivalent to ______


The statement, 'If I go to school, then I will get knowledge' is equivalent to ______ 


Which of the following is logically equivalent to `∼(∼p \implies q)`?


If p, q are true statements and r, s are false statements, then write the truth value of the compound statement

(p `→` ∼ r) `→` (q ∧ s)


If a statement b has truth value False and \[(p\wedge q)\leftrightarrow r\] has truth value True, then which of the following has truth value True?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×