Advertisements
Advertisements
Question
Check the validity of the statements:
r: 100 is a multiple of 4 and 5.
Solution
Let p: r ∧ s
Where r: “100 is a multiple of 4” is true
s: “100 is a multiple of 5” is true
Hence p is true.
APPEARS IN
RELATED QUESTIONS
Show that the statement
p: “If x is a real number such that x3 + 4x = 0, then x is 0” is true by
(i) direct method
(ii) method of contradiction
(iii) method of contrapositive
Find out the sentence are statement and are not. Justify your answer.
Two non-empty sets have always a non-empty intersection.
Write the negation of the statement:
Banglore is the capital of Karnataka.
Write the negation of the statement:
Ravish is honest.
I will not go to school.
Write the component statement of the compound statement and check whether the compound statement is true or false:
To enter into a public library children need an identity card from the school or a letter from the school authorities.
Write of the statement in the form "if p, then q".
There is traffic jam whenever it rains.
Check the validity of the statement:
p : 100 is a multiple of 4 and 5.
Check the validity of the statement:
q : 125 is a multiple of 5 and 7.
Check the validity of the statement:
r : 60 is a multiple of 3 or 5.
Which of the following statements are compound statements
“2 is both an even number and a prime number”
Translate the following statements in symbolic form
Tigers are found in Gir forest or Rajaji national park.
Which of the following sentences are statements? Justify
0 is a complex number.
Which of the following sentences are statements? Justify
y + 9 = 7.
Which of the following sentences are statements? Justify
Every square is a rectangle.
Find the component statements of the following compound statements.
The number 100 is divisible by 3, 11 and 5.
Find the component statements of the following compound statements.
`sqrt(7)` is a rational number or an irrational number.
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
Students can take Hindi or English as an optional paper.
Write down the negation of following compound statements
x = 2 and x = 3 are roots of the Quadratic equation x2 – 5x + 6 = 0.
Write down the negation of following compound statements
A triangle has either 3-sides or 4-sides.
Write down the negation of following compound statements
All prime integers are either even or odd.
Write down the negation of following compound statements
|x| is equal to either x or – x.
Rewrite the following statements in the form of conditional statements
The square of an odd number is odd.
Rewrite the following statements in the form of conditional statements
The unit digit of an integer is 0 or 5 if it is divisible by 5.
Form the biconditional statement p ↔ q, where
p: A triangle is an equilateral triangle.
q: All three sides of a triangle are equal.
Which of the following is a statement?
The negation of the statement “A circle is an ellipse” is ______.
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?
