Advertisements
Advertisements
प्रश्न
The contrapositive of the statement “If p, then q”, is ______.
पर्याय
If q, then p
If p, then ~ q
If ~ q, then ~ p
If ~ p, then ~ q
Advertisements
उत्तर
The contrapositive of the statement “If p, then q”, is if ~ q, then ~ p.
Explanation:
Here the statement is “If p, then q”
i.e. p → q
Contrapositive of the statement p → q is (~ q) → (~ p)
i.e., If ~ q, then ~ p.
APPEARS IN
संबंधित प्रश्न
Write the contrapositive and converse of the following statements.
If x is a prime number, then x is odd
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:
r: If it is hot outside, then you feel thirsty.
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.
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:
If it is hot outside, then you feel thirsty.
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.
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 he has courage he will win.
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.
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.
Which of the following is the converse of the statement?
“If Billu secure good marks, then he will get a bicycle.”
Write down the contrapositive of the following statements:
If n is a natural number, then n is an integer.
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 it snows, then the weather will be cold.
Write down the converse of following statements:
If all three angles of a triangle are equal, then the triangle is equilateral.
Write down the converse of following statements:
If x : y = 3 : 2, then 2x = 3y.
Write down the converse of following statements:
If S is a cyclic quadrilateral, then the opposite angles of S are supplementary
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 statement “If x2 is not even, then x is not even” is converse of the statement ______.
The contrapositive of statement ‘If Chandigarh is capital of Punjab, then Chandigarh is in India’ is ______.
Write the statement in the form “if p, then q”.
q: There is a traffic jam whenever it rains.
