Advertisements
Advertisements
Question
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.
Advertisements
Solution
You get an A grade if and only if you do all the homework regularly.
RELATED QUESTIONS
Write the contrapositive and converse of the following statements.
x is an even number implies that x is divisible by 4
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:
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.
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 a quadrilateral is a parallelogram, then its diagonals bisect each other.
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:
If Mohan is a poet, then he is poor.
Determine the contrapositive of the statement:
If she works, she will earn money.
Determine the contrapositive of the statement:
If Ravish skis, then it snowed.
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:
If x is an integer and x2 is odd, then x is odd.
Check whether the statement are true or not:
p : If x and y are odd integers, then x + y is an even integer.
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.
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 all three sides of a triangle are equal, then the triangle is equilateral.
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 a rectangle ‘R’ is a square, then R is a rhombus.
Write down the converse of following statements:
If the sum of squares of two sides of a triangle is equal to the square of third side of a triangle, then the triangle is right-angled.
Write down the converse of following statements:
If two triangles are similar, then the ratio of their corresponding sides are equal.
Using contrapositive method prove that if n2 is an even integer, then n is also an even integers.
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.
Write the statement in the form “if p, then q”.
q: There is a traffic jam whenever it rains.
