Advertisements
Advertisements
प्रश्न
Write the component statements of the following compound statements and check whether the compound statement is true or false.
57 is divisible by 2 or 3.
विकल्प
True
False
उत्तर
This statement is True.
Explanation:
Here the given statement is the form p v q which has the truth value T whenever either p or q or both have the truth value T.
Hence, it is a true statement and its component statements are
p: 57 is divisible by 2. ......(False)
q: 57 is divisible by 3. ......(True)
APPEARS IN
संबंधित प्रश्न
Find out the sentence are statement and are not. Justify your answer.
x2 + 5 | x | + 6 = 0 has no real roots.
Write the negation of the statement:
The earth is round.
Some even integers are prime.
There is a complex number which is not a real number.
Are the pair of statement are negation of each other:
The number x is not a rational number.
The number x is an irrational number.
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.
Find the component statement of the compound statement:
The sky is blue and the grass is green.
Determine whether the compound statement are true or false:
Delhi is in India and 2 + 2 = 5.
Negate of the statement :
There exists a number which is equal to its square.
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.
statement are true and false? In each case give a valid reason for saying so
s : If x and y are integers such that x > y, then − x < − y.
Determine whether the argument used to check the validity of the following statement is correct:
p : "If x2 is irrational, then x is rational"
The statement is true because the number x2 = π2 is irrational, therefore x = π is irrational.
Write the negation of the following statements:
x + y = y + x and 29 is a prime number.
Rewrite the following statements in the form of conditional statements:
When you sing, my ears hurt.
Translate the following statements in symbolic form:
If x = 7 and y = 4” then x + y = 11.
Identify the quantifiers and write the negation of the following statements:
For all even integers x, x2 is also even.
Which of the following sentences are statements? Justify
A triangle has three sides.
Which of the following sentences are statements? Justify
Sum of opposite angles of a cyclic quadrilateral is 180°.
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.
24 is a multiple of 4 and 6.
Translate the following statements into symbolic form
x and y are even integers.
Translate the following statements into symbolic form
A number is either divisible by 2 or 3.
Rewrite the following statements in the form of conditional statements
You will get a sweet dish after the dinner.
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.
Identify the Quantifiers in the following statements.
There exists a statement in above statements which is not true.
The negation of the statement “The product of 3 and 4 is 9” is ______.
