Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
(a) (i) This is the contrapositive of the given statement (a).
(ii) This is the converse of the given statement (a).
(b) (i) This is the contrapositive of the given statement (b).
(ii) This is the converse of the given statement (b).
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.
It the two lines are parallel, then they do not intersect in the same plane.
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.
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.
Write each of the following statement in the form “if-then”.
To get A+ in the class, it is necessary that you do the exercises of the book.
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”.
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:
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".
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:
Only if Max studies will he pass the test.
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.
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 natural number n is divisible by 6, then n is divisible by 2 and 3.
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 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.
Using contrapositive method prove that if n2 is an even integer, then n is also an even integers.
The converse of the statement “If x > y, then x + a > y + a” is ______.
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.
