हिंदी

Write the negation of the following. An angle is a right angle if and only if it is of measure 90°.

Advertisements
Advertisements

प्रश्न

Write the negation of the following.

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

योग
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 the 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
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 1: Mathematical Logic - Miscellaneous Exercise 1 [पृष्ठ ३२]

APPEARS IN

बालभारती Mathematics and Statistics 1 (Commerce) [English] Standard 12 Maharashtra State Board
अध्याय 1 Mathematical Logic
Miscellaneous Exercise 1 | Q 4.1 | पृष्ठ ३२

वीडियो ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्न

Express the following statement in symbolic form.

Mango is a fruit but potato is a vegetable.


Express the following statement in symbolic form.

I like playing but not singing.


Write the truth value of the negation of the following statement.

For every x ∈ N, x + 3 < 8.


Find the truth value of the following statement.

3 is a prime number and an odd number.


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.


If p : He swims

q : Water is warm

Give the verbal statement for the following symbolic statement.

q → p


Let p : Sachin wins the match.
q : Sachin is a member of Rajya Sabha.
r : Sachin is happy.
Write the verbal statement of the following.

p → q


Rewrite the following statement without using conditional –
(Hint : p → q ≡ ∼ p ∨ q)

If price increases, then demand falls.


Write the negation of the following.

If ∆ABC is not equilateral, then it is not equiangular.


Write the negation of the following.

If x ∈ A ∩ B, then x ∈ A and x ∈ B.


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

If it rains then the principal declares a holiday.


Write the negation of the following statement.

∃ x ∈ A, such that x + 5 < 11.


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


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


Choose the correct alternative:

Negation of p → (p ˅ ~q) is


Negation of “Some men are animal” is ______.


If (p ∧ ~ r) → (~ p ∨ q) is a false statement, then respective truth values of p, q and r are ______.


The symbolic form of the following circuit is (where p, q represents switches S1 and S2 closed respectively)


Which of the following is false?


The Boolean expression ∼(q ⇒ ∼p) is equivalent to: ______


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


Write the converse, inverse, and contrapositive of the statement. "If 2 + 5 = 10, then 4 + 10 = 20."


Write the contrapositive of the inverse of the statement:

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


Using the statements

p: Seema is fat,

q: Seema is happy,

Write the following statements in symbolic form;

  1. Seema is thin and happy.
  2. If Seema is fat then she is unhappy.

Using truth table prove that:

~ (p `leftrightarrow` q) ≡ (p ∧ ~ q) ∨ (q ∧ ~ p)


Construct the truth table for the statement pattern:

[(p → q) ∧ q] → p


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×