English

Determine Whether the Compound Statement Are True Or False: Delhi is in England and 2 + 2 = 4. - Mathematics

Advertisements
Advertisements

Question

Determine whether the compound statement are true or false:

 Delhi is in England and 2 + 2 = 4.
 

True or False

Solution

 False
The first component statement "Delhi is in England" is false. Since the connective is "and" and one component statement is false, the compound statement is false.

shaalaa.com
  Is there an error in this question or solution?
Chapter 31: Mathematical reasoning - Exercise 31.3 [Page 14]

APPEARS IN

RD Sharma Mathematics [English] Class 11
Chapter 31 Mathematical reasoning
Exercise 31.3 | Q 4.2 | Page 14

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

Show that the statement

p: “If x is a real number such that x3 + 4= 0, then x is 0” is true by

(i) direct method

(ii) method of contradiction

(iii) method of contrapositive


Show that the statement “For any real numbers a and ba2 = b2 implies that a = b” is not true by giving a counter-example.


Find out the sentence are statement and are not. Justify your answer.

There are 35 days in a month.


Write the negation of the statement:

 It rained on July 4, 2005.


Write the negation of the statement:

 The earth is round.


There is a complex number which is not a real number.


Write the negation of the statement:

 p : For every positive real number x, the number (x − 1) is also positive.

 


Write the negation of the statement:

q : For every real number x, either x > 1 or x < 1.


For statement, determine whether an inclusive "OR" or exclusive "OR" is used. Give reasons for your answer.

 To entry a country, you need a passport or a voter registration card.


For statement, determine whether an inclusive "OR" or exclusive "OR" is used. Give reasons for your answer.

A lady gives birth to a baby boy or a baby girl.


Write the component statement of the compound statement and check whether the compound statement is true or false:

The sand heats up quickly in the sun and does not cool down fast at night.

 

Determine whether the compound statement are true or false: 

 Delhi is in India and 2 + 2 = 5.


Determine whether the compound statement are true or false: 

Delhi is in England and 2 + 2 =5.

 

Write of the statement in the form "if p, then q". 

 It is necessary to have a passport to log on to the server.


Write of the statement in the form "if p, then q". 

 It rains only if it is cold.


Check the validity of the statement:

 r : 60 is a multiple of 3 or 5.

 

 statement are true and false? In each case give a valid reason for saying so

 t :  \[\sqrt{11}\]  is a rational number. 

 

 


Which of the following statements are compound statements 

“2 is both an even number and a prime number”


Write the truth value of the following statements.
(i) 9 is an even integer or 9 + 1 is even.
(ii) 2 + 4 = 6 or 2 + 4 = 7
(iii) Delhi is the capital of India and Islamabad is the capital of Pakistan.
(iv) Every rectangle is a square and every square is a rectangle
(v) The sun is a star or sun is a planet.


Translate the following biconditional into symbolic form:
“ABC is an equilateral triangle if and only if its each interior angle is 60°”


Identify the quantifiers and write the negation of the following statements:
There exists a number which is a multiple of 6 and 9.


The negation of the statement “It is raining and weather is cold.” is ______.


Which of the following sentences are statements? Justify

Sky is red.


Which of the following sentences are statements? Justify

15 + 8 > 23


Find the component statements of the following compound statements.

0 is less than every positive integer and every negative integer.


Find the component statements of the following compound statements.

Two lines in a plane either intersect at one point or they are parallel.


Find the component statements of the following compound statements.

A rectangle is a quadrilateral or a 5-sided polygon.


Translate the following statements into symbolic form

A number is either divisible by 2 or 3.


Write down the negation of following compound statements

All rational numbers are real and complex.


Write down the negation of following compound statements

All real numbers are rationals or irrationals.


Rewrite the following statements in the form of conditional statements

You will get a sweet dish after the dinner.


Rewrite the following statements in the form of conditional statements

You will fail, if you will not study.


Rewrite the following statements in the form of conditional statements

The square of a prime number is not prime.


Form the biconditional statement p ↔ q, where
p: The unit digit of an integer is zero.
q: It is divisible by 5.


Form the biconditional statement p ↔ q, where
p: A natural number n is odd.
q: Natural number n is not divisible by 2.


Identify the Quantifiers in the following statements.

For all negative integers x, x 3 is also a negative integers.


Which of the following is not a statement>


Which of the following statement is a conjunction?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×