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

Write the following compound statement symbolically. Hima Das wins gold medal if and only if she runs fast.

Advertisements
Advertisements

प्रश्न

Write the following compound statement symbolically. 

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

बेरीज
Advertisements

उत्तर

Let p: Hima Das wins gold medal

Let q: She runs fast.

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

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 1: Mathematical Logic - Exercise 1.1 [पृष्ठ ७]

APPEARS IN

व्हिडिओ ट्यूटोरियलVIEW ALL [3]

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)


Determine the truth values of p and q in the following case:

(p ∨ q) is T and (p ∧ q) is T


Determine the truth values of p and q in the following case:

(p ∨ q) is T and (p ∨ q) → q is F


Express the following statement in symbolic form.

Milk is white or grass is green.


Write the truth value of the following statement.

Earth is a planet and Moon is a star.


Write the truth value of the following statement.

16 is an even number and 8 is a perfect square.


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

London is in England.


Write the following statement in symbolic form.

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


Write the following statement in symbolic form.

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


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.

If Sunday is not holiday then Ram studies on holiday.


If p : He swims

q : Water is warm

Give the verbal statement for the following symbolic statement:

p ↔ ~ q


Fill in the blanks :

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


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.

3 is prime number if 3 is perfect square number.


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

To be brave is necessary and sufficient condition to climb the Mount Everest.


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.


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) ∨ r


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 → r


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

If a quadrilateral is rhombus then it is not a square.


Consider the following statements.

  1. If D is dog, then D is very good.
  2. If D is very good, then D is dog.
  3. If D is not very good, then D is not a dog.
  4. If D is not a dog, then D is not very good. 

Identify the pairs of statements having the same meaning. Justify.


Write the negation of the following statement.

7 is prime number and Tajmahal is in Agra.


Write the negation of the following statement.

∃ x ∈ A, such that x + 5 < 11.


Write the following compound statements symbolically.

Triangle is equilateral or isosceles


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)


Negation of “Some men are animal” is ______.


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.


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


Which of the following is false?


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


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


Express the following compound statement symbolically:

Delhi is in India but Dhaka is not in Sri Lanka


Using truth table prove that:

~ (p `leftrightarrow` q) ≡ (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×