Advertisements
Advertisements
Question
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.
Advertisements
Solution
The component statements of the given compound statement are:
1) To enter into a public library, children need an identity card from the school.
2) To enter into a public library, children need a letter from the school authorities.
The compound statement is true because both component statements are true.
RELATED QUESTIONS
Find out the sentence are statement and are not. Justify your answer.
All triangles have three sides.
Find out the sentence are statement and are not. Justify your answer.
The product of (−1) and 8 is 8.
Give three examples of sentences which are not statements. Give reasons for the answers.
Write the negation of the statement:
Banglore is the capital of Karnataka.
Both the diagonals of a rectangle have the same length.
All policemen are thieves.
Are the pair of statement are negation of each other:
The number x is not a rational number.
The number x is not an irrational number.
Write the negation of the statement:
p : For every positive real number x, the number (x − 1) is also positive.
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.
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.
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.
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 = 4.
Write of the statement in the form "if p, then q".
It is necessary to be rich in order to be happy.
Write of the statement in the form "if p, then q".
Whenever it rains it is cold.
Check the validity of the statement:
q : 125 is a multiple of 5 and 7.
statement are true and false? In each case give a valid reason for saying so
p : Each radius of a circle is a chord of the circle.
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.
Which of the following statements are compound statements
“Ram and Rahim are friends”
Translate the following statements in symbolic form
2 and 3 are prime numbers
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.
Rewrite the following statements in the form of conditional statements:
Ramesh will get dessert only if he eats his dinner.
Rewrite the following statements in the form of conditional statements:
When you sing, my ears hurt.
Rewrite the following statements in the form of conditional statements:
A sufficient condition for Tara to visit New Delhi is that she goes to the Rashtrapati Bhawan.
Express in English, the statement p → q, where
p: It is raining today
q: 2 + 3 > 4
Identify the quantifiers and write the negation of the following statements:
For all even integers x, x2 is also even.
The negation of the statement “It is raining and weather is cold.” is ______.
Which of the following sentences are statements? Justify
Every set is an infinite set.
Which of the following sentences are statements? Justify
Every square is a rectangle.
Find the component statements of the following compound statements.
Plants use sunlight, water and carbon dioxide for photosynthesis.
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
All prime integers are either even or odd.
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.
There exists a real number x such that x2 + 1 = 0.
The negation of the statement “Rajesh or Rajni lived in Bangalore” is ______.
Which of the following statement is a conjunction?
