Advertisements
Advertisements
प्रश्न
State the converse and contrapositive of statement:
If a quadrilateral is a parallelogram, then its diagonals bisect each other.
Advertisements
उत्तर
Converse of the given statement:
If the diagonals of a quadrilateral bisect each other, then it is a parallelogram.
Contrapositive of the given statement:
If the diagonals of a quadrilateral do not bisect each other, then it is not a parallelogram.
APPEARS IN
संबंधित प्रश्न
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.
Something is cold implies that it has low temperature.
Write the contrapositive and converse of the following statements.
You cannot comprehend geometry if you do not know how to reason deductively.
Write each of the following statement in the form “if-then”.
The Banana trees will bloom if it stays warm for a month.
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:
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.
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.
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 you live in Delhi, then you have winter clothes.
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 she works, she will earn money.
Determine the contrapositive of the statement:
It never rains when it is cold.
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.
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 it snows, then the weather will be cold.
Write down the converse of following statements:
If a rectangle ‘R’ is a square, then R is a rhombus.
Write down the converse of following statements:
If today is Monday, then tomorrow is Tuesday.
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 is zero, then x is neither positive nor negative.
Using contrapositive method prove that if n2 is an even integer, then n is also an even integers.
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 ______.
