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महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता १२ वी

Write the following statements in symbolic form Even though it is not cloudy, it is still raining - Mathematics and Statistics

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प्रश्न

Write the following statements in symbolic form

Even though it is not cloudy, it is still raining

बेरीज
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उत्तर

Let p: It is cloudy.

q: It is still raining.

∴ The symbolic form of the given statement is ~p ∧ q

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पाठ 1.1: Mathematical Logic - Long Answers II

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


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.


Construct the truth table of the following statement pattern.

(p ∧ ∼q) ↔ (p → q)


Construct the truth table of the following statement pattern.

p → [∼ (q ∧ r)]


Construct the truth table of the following statement pattern.

(p ∨ ∼ q) → (r ∧ p)


Express the following statement in symbolic form.

e is a vowel or 2 + 3 = 5


Express the following statement in symbolic form.

I like playing but not singing.


Write the negation of the following statement.

− 3 is a natural number.


Write the following statement in symbolic form.

Stock prices are high if and only if stocks are rising.


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

~ [(~ p ∨ s) ∧ (~ q ∧ r)]


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

(p → q) ↔ ~(p ∨ q)


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.

q → p


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.

x3 + y3 = (x + y)3 if xy = 0.


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

The drug is effective though it has side effects.


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.


If p : Proof is lengthy.
q : It is interesting.
Express the following statement in symbolic form.

If proof is lengthy then it is interesting.


If p : Proof is lengthy.
q : It is interesting.
Express the following statement in symbolic form.

It is interesting iff the proof is lengthy.


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


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


Write the negation of the following.

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


Write the negation of the following.

If x ∈ A ∩ B, then x ∈ A and x ∈ B.


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 following compound statements symbolically.

Triangle is equilateral or isosceles


Without using truth table prove that:

~ (p ∨ q) ∨ (~ p ∧ q) ≡ ~ p


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


Write the following statement in symbolic form:

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


State whether the following statement is True or False:

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


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?


Let p : 7 is not greater than 4 and q : Paris is in France by two statements. Then ∼(p ∨ q) is the statement ______ 


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


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


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


Conditional of p → q is equivalent to p → ∼ q.


Write the following statement in symbolic form.

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


Write the following statement in symbolic form.

4 is an odd number if 3 is not a prime factor of 6.


The statement ∼(p ↔ ∼q) is ______.


Write the negation of (p `leftrightarrow` q).


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