मराठी

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.

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प्रश्न

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.

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उत्तर

You watch television if and only if your mind is free.

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पाठ 31: Mathematical reasoning - Exercise 31.5 [पृष्ठ २१]

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आर.डी. शर्मा Mathematics [English] Class 11
पाठ 31 Mathematical reasoning
Exercise 31.5 | Q 3.1 | पृष्ठ २१

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संबंधित प्रश्‍न

Write the contrapositive and converse of the following statements.

x is an even number implies that x is divisible by 4


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A quadrilateral is a parallelogram if its diagonals bisect each other.


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:

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”.

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:

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.


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 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:

If it snows, then they do not drive the car.


Determine the contrapositive of the statement:

 It never rains when it is cold.


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 If Ravish skis, then it snowed.


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If x is less than zero, then x is not positive.


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 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.


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 q : If xy 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.


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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.


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If x is a real number such that 0 < x < 1, then x2 < 1.


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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 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 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 contrapositive of the statement “If 7 is greater than 5, then 8 is greater than 6” is ______.


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Write the statement in the form “if p, then q”.

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Write the statement in the form “if p, then q”.

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