English

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.

Advertisements
Advertisements

Question

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.

Sum
Advertisements

Solution

Let p : A real number is not rational.
q : A real number must be irrational.

The symbolic form is p → q.

shaalaa.com
  Is there an error in this question or solution?
Chapter 1: Mathematical Logic - Miscellaneous Exercise 1 [Page 32]

APPEARS IN

Balbharati Mathematics and Statistics 1 (Commerce) [English] Standard 12 Maharashtra State Board
Chapter 1 Mathematical Logic
Miscellaneous Exercise 1 | Q 4.03 | Page 32

Video TutorialsVIEW ALL [2]

RELATED QUESTIONS

Using truth table prove that p ↔ q = (p ∧ q) ∨ (~p ∧ ~q).


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


Construct the truth table of the following statement pattern.

(p ∧ q) ↔ (q ∨ r)


Construct the truth table of the following statement pattern.

∼ p ∧ [(p ∨ ∼ q) ∧ q]


Construct the truth table of the following statement pattern.

(p ∨ ∼ q) → (r ∧ p)


Construct the truth table of the following:

p → (q → p)


Construct the truth table of the following:

[(∼p ∨ q) ∧ (q → r)] → (p → r)


Write the truth value of the following statement.

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


Find the truth value of the following statement.

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


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.

3 is prime number if 3 is perfect square number.


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 ∨ r)


Write the negation of the following.

If ∆ABC is not equilateral, then it is not equiangular.


Write the negation of the following.

Ramesh is intelligent and he is hard working.


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.


Find the negation of 10 + 20 = 30


Write the following compound statements symbolically.

Triangle is equilateral or isosceles


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

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°”


Given 'p' and 'q' as true and 'r' as false, the truth values of p v (q ∧ ~r) and (p → r) ∧ q are respectively


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


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


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


Write the contrapositive of the inverse of the statement:

‘If two numbers are not equal, then their squares are not equal’.


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×