हिंदी

Write down the contrapositive of the following statements: If x and y are negative integers, then xy is positive. - Mathematics

Advertisements
Advertisements

प्रश्न

Write down the contrapositive of the following statements:

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

योग
Advertisements

उत्तर

We know that the contrapositive of p → q is (~ q) → (~ p)

If xy is not positive integer, then x or y is not negative integer.

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 14: Mathematical Reasoning - Exercise [पृष्ठ २६४]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics [English] Class 11
अध्याय 14 Mathematical Reasoning
Exercise | Q 9.(iv) | पृष्ठ २६४

वीडियो ट्यूटोरियलVIEW ALL [1]

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.


Write the contrapositive and converse of the following statements.

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


Write each of the following statement in the form “if-then”.

The Banana trees will bloom if it stays warm for a month.


Write each of the following statement in the form “if-then”.

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


Write each of the following statement in the form “if-then”.

To get A+ in the class, it is necessary that you do the exercises of the book.


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”.

q: For you to get an A grade, it is necessary and sufficient that you do all the homework regularly.


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.


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.


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.


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 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:

 If Ravish skis, then it snowed.


Determine the contrapositive of the statement:

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


Determine the contrapositive of the statement:

 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.


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.


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


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 ______.


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


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”.

q: There is a traffic jam whenever it rains.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×