Advertisements
Advertisements
प्रश्न
The contrapositive of statement ‘If Chandigarh is capital of Punjab, then Chandigarh is in India’ is ______.
पर्याय
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
उत्तर
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
संबंधित प्रश्न
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”.
The Banana trees will bloom if it stays warm for a month.
Write each of the following statement in the form “if-then”.
A quadrilateral is a parallelogram if its diagonals bisect each other.
Given statements in (a) and (b). Identify the statements given below as contrapositive or converse of each other.
(a) If you live in Delhi, then you have winter clothes.
(i) If you do not have winter clothes, then you do not live in Delhi.
(ii) If you have winter clothes, then you live in Delhi.
(b) If a quadrilateral is a parallelogram, then its diagonals bisect each other.
(i) If the diagonals of a quadrilateral do not bisect each other, then the quadrilateral is not a parallelogram.
(ii) If the diagonals of a quadrilateral bisect each other, then it is a parallelogram.
State the converse and contrapositive of each of the following statements:
q: I go to a beach whenever it is a sunny day.
Write the statement in the form “if p, then q”.
r: You can access the website only if you pay a subscription fee.
Re write each of the following statements 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.
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.
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:
A positive integer is prime only if it has no divisors other than 1 and itself.
State the converse and contrapositive of statement:
If you live in Delhi, then you have winter clothes.
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.
Rewrite of the statement in the form "p if and only if q".
r : For you to get an A grade, it is necessary and sufficient that you do all the homework regularly.
Determine the contrapositive of the statement:
It never rains when it is cold.
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:
q : If x, y are integers such that xy is even, then at least one of x and 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 x = y and y = 3, then x = 3.
Write down the contrapositive of the following statements:
If x and y are negative integers, then xy is positive.
Write down the contrapositive of the following statements:
If natural number n is divisible by 6, then n is divisible by 2 and 3.
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 today is Monday, then tomorrow is Tuesday.
Write down the converse of following statements:
If x : y = 3 : 2, then 2x = 3y.
Write down the converse of following statements:
If x is zero, then x is neither positive nor negative.
The contrapositive of the statement “If 7 is greater than 5, then 8 is greater than 6” is ______.
The converse of the statement “If sun is not shining, then sky is filled with clouds” 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.
