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

Write the negation of p → q - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

Write the negation of p → q

बेरीज
Advertisements

उत्तर

∼ p → q ≡  (∼p ∨ q)   .......[∵ p → q ≡ ∼p ∨ q]

≡ ∼ (∼p) ∨ ∼ q       .......[De’Morgan’s Law]

≡ ∼ ∼ p ∧ ∼ q

≡  p ∧ ∼ q

≡ p ∧ (∼q)

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

व्हिडिओ ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्‍न

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

[~(~p ∧ ~q)] v q


Using truth table, prove the following logical equivalence:

(p ∧ q) → r ≡ p → (q → r)


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 ∨ r)


Construct the truth table of the following statement pattern.

p → [∼ (q ∧ r)]


Construct the truth table of the following statement pattern.

(∼ p → ∼ q) ∧ (∼ q → ∼ p)


If p ∧ q is false and p ∨ q is true, then ______ is not true.


Construct the truth table of the following:

∼ (∼p ∧ ∼q) ∨ q


Construct the truth table of the following:

[(∼p ∨ q) ∧ (q → r)] → (p → r)


Express the following statement in symbolic form.

I like playing but not singing.


Write the truth value of the following statement.

A quadratic equation has two distinct roots or 6 has three prime factors.


Write the following statement in symbolic form.

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


Find the truth value of the following statement.

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


Find the truth value of the following statement.

If a joint venture is a temporary partnership, then discount on purchase is credited to the supplier.


Find the truth value of the following statement.

Every accountant is free to apply his own accounting rules if and only if machinery is an asset.


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

(p → q) ∨ (r ∧ s) 


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 a holiday and Ram studies on holiday.


If p : He swims

q : Water is warm

Give the verbal statement for the following symbolic statement.

q ∧ ~ p


Negation of “some men are animal” is ______.


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.

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 a real number is not rational, then it must be irrational.


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 → q


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


Write the negation of the following.

Kanchanganga is in India and Everest is in Nepal.


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

If 10 − 3 = 7 then 10 × 3 ≠ 30.


Write the negation of the following statement.

7 is prime number and Tajmahal is in Agra.


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


Write the following statements in symbolic form

Even though it is not cloudy, it is still raining


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


If p, q are true statement and r is false statement, then which of the following statements is a true statement.


Which of the following is false?


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


Which of the following is NOT true for p → q.


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


Let p, q and r be any three logical statements. Which of the following is true?


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


The statement ∼(p ↔ ∼q) is ______.


Express the following compound statement symbolically:

Delhi is in India but Dhaka is not in Sri Lanka


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×