Advertisements
Advertisements
Question
Identify the component statements and the connective in the following compound statements.
2 is a positive number or a negative number.
Advertisements
Solution
The component statements are given by
p: 2 is a positive number
q: 2 is a negative number
The connective is ‘or’
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.
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.
Mathematics is difficult.
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.
Some even integers are prime.
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.
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 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 negation of statement:
There exists x ϵ N, x + 3 = 10
Negate of the statement :
There exists a number which is equal to its square.
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".
It is necessary to have a passport to log on to the server.
Write of the statement in the form "if p, then q".
It is necessary to be rich in order to be happy.
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.
Translate the following statements in symbolic form
Tigers are found in Gir forest or Rajaji national park.
Write negation of the statement
“Everyone who lives in India is an Indian”
Write the negation of the following statements:
p: All triangles are equilateral triangles.
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:
Mohan will be a good student if he studies hard.
Express in English, the statement p → q, where
p: It is raining today
q: 2 + 3 > 4
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:
There exists a number which is equal to its square.
The negation of the statement “It is raining and weather is cold.” is ______.
Which of the following sentences are statements? Justify
Sky is red.
Find the component statements of the following compound statements.
`sqrt(7)` is a rational number or an irrational number.
Find the component statements of the following compound statements.
Plants use sunlight, water and carbon dioxide for photosynthesis.
Translate the following statements into symbolic form
x and y are even integers.
Translate the following statements into symbolic form
Either x or x + 1 is an odd integer.
Translate the following statements into symbolic form
Either x = 2 or x = 3 is a root of 3x 2 – x – 10 = 0
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.
Form the biconditional statement p ↔ q, where
p: A triangle is an equilateral triangle.
q: All three sides of a triangle are equal.
Identify the Quantifiers in the following statements.
There exists a statement in above statements which is not true.
Identify the Quantifiers in the following statements.
There exists a real number x such that x2 + 1 = 0.
Check the validity of the following statement.
p: 125 is divisible by 5 and 7.
The negation of the statement “101 is not a multiple of 3” is ______.
