Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
Statement p can be written as follows.
If a positive integer is prime, then it has no divisors other than 1 and itself.
The converse of the statement is as follows.
If a positive integer has no divisors other than 1 and itself, then it is prime.
The contrapositive of the statement is as follows.
If positive integer has divisors other than 1 and itself, then it is not prime.
संबंधित प्रश्न
Write the contrapositive and converse of the following statements.
Something is cold implies that it has low temperature.
Write each of the following statement in the form “if-then”.
You get a job implies that your credentials are good.
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.
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”.
r: If a quadrilateral is equiangular, then it is a rectangle and if a quadrilateral is a rectangle, then it is equiangular.
State the converse and contrapositive of statement:
If it is hot outside, then you feel thirsty.
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".
s : If a tumbler is half empty, then it is half full and if a tumbler is half full, then it is half empty.
Determine the contrapositive of the statement:
If Mohan is a poet, then he is poor.
Determine the contrapositive of the statement:
If x is less than zero, then x is not positive.
Determine the contrapositive of the statement:
If he has courage he will 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.
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 all three sides of a triangle are equal, then the triangle is equilateral.
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 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 you go to Agra, then you must visit Taj Mahal.
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 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 converse of the statement “If x > y, then x + a > y + a” 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.
