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

Express the following statement in symbolic form. Even though it is cloudy, it is still raining.

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प्रश्न

Express the following statement in symbolic form.

Even though it is cloudy, it is still raining.

एका वाक्यात उत्तर
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उत्तर

Let p : It is cloudy.

q : It is still raining.

The symbolic form is p ∧ q.

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पाठ 1: Mathematical Logic - Exercise 1.2 [पृष्ठ ६]

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संबंधित प्रश्‍न

Using the truth table, prove the following logical equivalence :

p ↔ q ≡ (p ∧ q) ∨ (~p ∧ ~q)


Write the following compound statement symbolically.

Nagpur is in Maharashtra and Chennai is in Tamil Nadu. 


Construct the truth table of the following statement pattern.

(p ∧ ∼q) ↔ (p → q)


Express the following statement in symbolic form.

e is a vowel or 2 + 3 = 5


Write the truth value of the following statement.

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


Write the negation of the following statement.

All men are animals.


Write the negation of the following statement.

− 3 is a natural number.


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.

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


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


Fill in the blanks :

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


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.


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

If demand falls, then price does not increase.


Write the negation of the following.

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


The negation of the statement (p ˄ q) `→` (r ˅ ∼ p) is ______.


Without using truth table prove that:

~ (p ∨ q) ∨ (~ p ∧ q) ≡ ~ p


Write the following statements in symbolic form

Even though it is not cloudy, it is still raining


Without using truth table show that -

(p ˅ q) ˄ (∼p v ∼q) ≡ (p ∧ ∼q) ˄ (∼p ∧ q)


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 ______.


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


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


The statement ∼(p ↔ ∼q) is ______.


From the following set of statements, select two statements which have similar meaning.

  1. If a man is judge, then he is honest.
  2. If a man is not a judge, then he is not honest.
  3. If a man is honest, then he is a judge.
  4. If a man is not honest, then he is not a judge.

Write the negation of p ↔ q.


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