Advertisements
Advertisements
Question
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.
Options
True
False
Advertisements
Solution
This statement is True.
Explanation:
It is true statements and its component statements are
p: 2 is an even number. .....(True)
q: 2 is a prime number. ......(True)
APPEARS IN
RELATED QUESTIONS
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.
Find out the sentence are statement and are not. Justify your answer.
Two non-empty sets have always a non-empty intersection.
Find out the sentence are statement and are not. Justify your answer.
Every rhombus is a square.
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.
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 earth is round or the sun is cold.
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:
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:
Square of an integer is positive or negative.i
Write the negation of statement:
For every x ϵ N, x + 3 < 10
Negate statement:
All the students completed their homework.
Write of the statement in the form "if p, then q".
It rains only if it is cold.
Write of the statement in the form "if p, then q".
Whenever it rains it is cold.
Check the validity of the statement:
p : 100 is a multiple of 4 and 5.
Which of the following statements are compound statements
“9 is neither an even number nor a prime number”
Identify the component statements and the connective in the following compound statements.
It is raining or the sun is shining.
Translate the following statements in symbolic form
2 and 3 are prime numbers
Translate the following statements in symbolic form:
If x = 7 and y = 4” then x + y = 11.
The negation of the statement “It is raining and weather is cold.” is ______.
Which of the following sentences are statements? Justify
A triangle has three sides.
Which of the following sentences are statements? Justify
0 is a complex number.
Which of the following sentences are statements? Justify
Sky is red.
Which of the following sentences are statements? Justify
Every square is a rectangle.
Which of the following sentences are statements? Justify
Sum of opposite angles of a cyclic quadrilateral is 180°.
Write down the negation of following compound statements
All real numbers are rationals or irrationals.
Write down the negation of following compound statements
6 is divisible by 2 and 3.
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.
Rewrite the following statements in the form of conditional statements
2b = a + c, if a, b and c are in A.P.
Form the biconditional statement p ↔ q, where
p: The unit digit of an integer is zero.
q: It is divisible by 5.
Identify the Quantifiers in the following statements.
For every natural number x, x + 1 is also a natural number.
Identify the Quantifiers in the following statements.
There exists a triangle which is not an isosceles triangle.
Check the validity of the following statement.
p: 125 is divisible by 5 and 7.
Which of the following is a statement?
