Advertisements
Advertisements
Question
The contrapositive of statement ‘If Chandigarh is capital of Punjab, then Chandigarh is in India’ is ______.
Options
If Chandigarh is not in India, then Chandigarh is not the capital of Punjab
If Chandigarh is in India, then Chandigarh is Capital of Punjab
If Chandigarh is not capital of Punjab, then Chandigarh is not capital of India
If Chandigarh is capital of Punjab, then Chandigarh is not in India
Advertisements
Solution
The contrapositive of statement ‘If Chandigarh is capital of Punjab, then Chandigarh is in India’ is if Chandigarh is not in India, then Chandigarh is not the capital of Punjab.
Explanation:
Let p: Chandigarh is Capital of Punjab
and q: Chandigarh is in India
~ p: Chandigarh is not Capital of Punjab
~ q: Chandigarh is not in India
If (~ q), then (~ p)
i.e. If Chandigarh is not in India, then Chandigarh is not the Capital of Punjab.
APPEARS IN
RELATED QUESTIONS
Rewrite the following statement with “if-then” in five different ways conveying the same meaning.
If a natural number is odd, then its square is also odd.
Write the contrapositive and converse of the following statements.
If x is a prime number, then x is odd
Write the contrapositive and converse of the following statements.
x is an even number implies that x is divisible by 4
Write each of the following statement in the form “if-then”.
You get a job implies that your credentials are good.
State the converse and contrapositive of each of the following statements:
p: A positive integer is prime only if it has no divisors other than 1 and itself.
State the converse and contrapositive of each of the following statements:
q: I go to a beach whenever it is a sunny day.
State the converse and contrapositive of each of the following statements:
r: If it is hot outside, then you feel thirsty.
Re write each of the following statements in the form “p if and only if q”.
q: For you to get an A grade, it is necessary and sufficient that you do all the homework regularly.
Re write each of the following statements in the form “p if and only if q”.
r: If a quadrilateral is equiangular, then it is a rectangle and if a quadrilateral is a rectangle, then it is equiangular.
Given below are two statements
p: 25 is a multiple of 5.
q: 25 is a multiple of 8.
Write the compound statements connecting these two statements with “And” and “Or”. In both cases check the validity of the compound statement.
State the converse and contrapositive of statement:
I go to a beach whenever it is a sunny day.
State the converse and contrapositive of statement:
If you live in Delhi, then you have winter clothes.
State the converse and contrapositive of statement:
If a quadrilateral is a parallelogram, then its diagonals bisect each other.
Rewrite of the statement in the form "p if and only if q".
p : If you watch television, then your mind is free and if your mind is free, then you watch television.
Rewrite of the statement in the form "p if and only if q".
q : If a quadrilateral is equiangular, then it is a rectangle and if a quadrilateral is a rectangle, then it is equiangular.
Determine the contrapositive of the statement:
If Mohan is a poet, then he is poor.
Determine the contrapositive of the statement:
Only if Max studies will he pass the test.
Determine the contrapositive of the statement:
If x is less than zero, then x is not positive.
Determine the contrapositive of the statement:
It is necessary to be strong in order to be a sailor.
Determine the contrapositive of the statement:
Only if he does not tire will he win.
Determine the contrapositive of the statement:
If x is an integer and x2 is odd, then x is odd.
Check whether the statement are true or not:
p : If x and y are odd integers, then x + y is an even integer.
Show that the following statement is true.
p: For any real numbers x, y if x = y, then 2x + a = 2y + a when a ∈ Z.
Write down the contrapositive of the following statements:
If it snows, then the weather will be cold.
Write down the converse of following statements:
If you go to Agra, then you must visit Taj Mahal.
Write down the converse of following statements:
If the sum of squares of two sides of a triangle is equal to the square of third side of a triangle, then the triangle is right-angled.
Write down the converse of following statements:
If all three angles of a triangle are equal, then the triangle is equilateral.
Using contrapositive method prove that if n2 is an even integer, then n is also an even integers.
The contrapositive of the statement “If 7 is greater than 5, then 8 is greater than 6” is ______.
The converse of the statement “If x > y, then x + a > y + a” is ______.
The contrapositive of the statement “If p, then q”, is ______.
Write the statement in the form “if p, then q”.
p: It is necessary to have a password to log on to the server.
Write the statement in the form “if p, then q”.
q: There is a traffic jam whenever it rains.
