Advertisements
Advertisements
Question
Determine whether the compound statement are true or false:
Delhi is in India and 2 + 2 = 5.
Advertisements
Solution
False
The second component statement "2 plus 2 equals 5" is false. Since the connective is "and" and one component statement is false, the compound statement is false.
APPEARS IN
RELATED QUESTIONS
Show that the following statement is true by the method of contrapositive.
p: If x is an integer and x2 is even, then x is also even.
By giving a counter example, show that the following statements are not true.
p: If all the angles of a triangle are equal, then the triangle is an obtuse angled triangle.
By giving a counter example, show that the following statements are not true.
q: The equation x2 – 1 = 0 does not have a root lying between 0 and 2.
Find out the sentence are statement and are not. Justify your answer.
Every set is a finite set.
Find out the sentence are statement and are not. Justify your answer.
Is the earth round?
Find out the sentence are statement and are not. Justify your answer.
All real numbers are complex numbers.
Write the negation of the statement:
Banglore is the capital of Karnataka.
Write the negation of the statement:
It rained on July 4, 2005.
There is a complex number which is not a real number.
I will not go to school.
Check whether the following pair of statements are negation of each other. Give reasons for your answer.
a + b = b + a is true for every real number a and b.
There exist real numbers a and b for which a + b = b + a.
Write the component statement of the compound statement and check whether the compound statement is true or false:
All rational numbers are real and all real numbers are not complex.
Write the component statement of the compound statement and check whether the compound statement is true or false:
x = 2 and x = 3 are the roots or the equation 3x2 − x − 10 = 0.
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".
There is traffic jam whenever it rains.
Write of the statement in the form "if p, then q".
The game is cancelled only if it is raining.
Write of the statement in the form "if p, then q".
It never rains when it is cold.
statement are true and false? In each case give a valid reason for saying so
q : The centre of a circle bisects each chord of the circle.
statement are true and false? In each case give a valid reason for saying so
r : Circle is a particular case of an ellipse.
statement are true and false? In each case give a valid reason for saying so
t : \[\sqrt{11}\] is a rational number.
Write negation of the statement
“Everyone who lives in India is an Indian”
Rewrite the following statements in the form of conditional statements:
Mohan will be a good student if he studies hard.
Rewrite the following statements in the form of conditional statements:
When you sing, my ears hurt.
Express in English, the statement p → q, where
p: It is raining today
q: 2 + 3 > 4
Translate the following biconditional into symbolic form:
“ABC is an equilateral triangle if and only if its each interior angle is 60°”
Which of the following sentences are statements? Justify
15 + 8 > 23
Find the component statements of the following compound statements.
Number 7 is prime and odd.
Write the component statements of the following compound statements and check whether the compound statement is true or false.
2 is an even number and a prime number.
Translate the following statements into symbolic form
Either x or x + 1 is an odd integer.
Translate the following statements into symbolic form
A number is either divisible by 2 or 3.
Form the biconditional statement p ↔ q, where
p: The unit digit of an integer is zero.
q: It is divisible by 5.
Check the validity of the following statement.
p: 125 is divisible by 5 and 7.
Which of the following is a statement?
Which of the following is not a statement>
The connective in the statement “Earth revolves round the Sun and Moon is a satellite of earth” is ______.
The negation of the statement “Plants take in CO2 and give out O2 ” is ______.
The negation of the statement “Rajesh or Rajni lived in Bangalore” is ______.
Which of the following statement is a conjunction?
State whether the following sentences are statements are not.
(i) The angles opposite to equal sides of a triangle are equal.
(ii) The moon is a satellite of earth.
(iii) May God bless you!
(iv) Asia is a continent.
(v) How are you?
