हिंदी

Rewrite the following statement without using the connective ‘If ... then’. If it rains then the principal declares a holiday. - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

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

If it rains then the principal declares a holiday.

योग

उत्तर

Let p : It rains.

q : The principal declares a holiday.

The given statement is p → q.

But p → q ≡ ~p ∨ q.

∴ The given statement can be written as ‘It does not rain or the principal declares a holiday’.

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 1: Mathematical Logic - Miscellaneous Exercise 1 [पृष्ठ ३३]

APPEARS IN

बालभारती Mathematics and Statistics 1 (Commerce) [English] 12 Standard HSC Maharashtra State Board
अध्याय 1 Mathematical Logic
Miscellaneous Exercise 1 | Q 4.17 | पृष्ठ ३३

वीडियो ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्न

Using truth table, prove the following logical equivalence:

(p ∧ q) → r ≡ p → (q → r)


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


Evaluate: ∫ x . log x dx


Write the following compound statement symbolically.

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


Construct the truth table of the following statement pattern.

[(p → q) ∧ q] → p


Construct the truth table of the following statement pattern.

p → [∼ (q ∧ r)]


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


Express the following statement in symbolic form.

Even though it is cloudy, it is still raining.


Write the truth value of the following statement.

Earth is a planet and Moon is a star.


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) 


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 : He swims

q : Water is warm

Give the verbal statement for the following symbolic statement.

p ↔ ~ q


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.

Kavita is brilliant and brave.


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.

It is not true that Ram is tall and handsome.


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.

It is not true that the proof is lengthy but it is interesting.


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 ∨ r)


Write the negation of the following.

Ramesh is intelligent and he is hard working.


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


Write the following compound statements symbolically.

Triangle is equilateral or isosceles


Choose the correct alternative:

A biconditional statement is the conjunction of two ______ statements


State whether the following statement is True or False:

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


Negation of “Some men are animal “ is ______


Write the following statements in symbolic form.

If Qutub – Minar is in Delhi then Taj-Mahal is in Agra


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)


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


Which of the following is false?


Let S be a non-empty subset of R. Consider the following statement:

p: There is a rational number x ∈ S such that x > 0. Which of the following statements is the negation of the statement p? 


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


Write the following statement in symbolic form.

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


Express the following compound statement symbolically:

3 + 8 ≥ 12 if and only if 5 × 4 ≤ 25


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×