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Determine the Contrapositive of the Statement: Only If Max Studies Will He Pass the Test.

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प्रश्न

Determine the contrapositive of the statement:

 Only if Max studies will he pass the test.

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उत्तर

 If Max does not study, then he will not pass the test.

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

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आर.डी. शर्मा Mathematics [English] Class 11
अध्याय 31 Mathematical reasoning
Exercise 31.5 | Q 4.02 | पृष्ठ २१

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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.


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If x is a prime number, then x is 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.

You cannot comprehend geometry if you do not know how to reason deductively.


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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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.


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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 you live in Delhi, then you have winter clothes.


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


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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.


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 If x is an integer and x2 is odd, then x is odd.

 

Check whether the statement are true or not: 

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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 n is a natural number, then n is an integer.


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If x and y are negative integers, then xy is positive.


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If natural number n is divisible by 6, then n is divisible by 2 and 3.


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If it snows, then the weather will be cold.


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If today is Monday, then tomorrow is Tuesday.


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If you go to Agra, then you must visit Taj Mahal.


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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.


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If x : y = 3 : 2, then 2x = 3y.


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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 statement “If x2 is not even, then x is not even” is converse of the statement ______.


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

q: There is a traffic jam whenever it rains.


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