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.
It the two lines are parallel, then they do not intersect in the same plane.
Write each of the following statement in the form “if-then”.
You get a job implies that your credentials are good.
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.
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.
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:
Only if Max studies will he pass the test.
Determine the contrapositive of the statement:
If it snows, then they do not drive the car.
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:
Only if he does not tire will he win.
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 all three sides of a triangle are equal, then the triangle is equilateral.
Write down the contrapositive of the following statements:
If it snows, then the weather will be cold.
Write down the contrapositive of the following statements:
If x is a real number such that 0 < x < 1, then x2 < 1.
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 you go to Agra, then you must visit Taj Mahal.
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 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.
Write down the converse of following statements:
If two triangles are similar, then the ratio of their corresponding sides are equal.
The contrapositive of the statement “If p, then q”, 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”.
p: It is necessary to have a password to log on to the server.
