Q9 of 69 Page 261

Write down the contrapositive of the following statements:

(i) If x = y and y = 3, then x = 3.


(ii) If n is a natural number, then n is an integer.


(iii) If all three sides of a triangle are equal, then the triangle is equilateral.


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


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


(vi) If it snows, then the weather will be cold.


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

(i) Definition of contrapositive: A conditional statement is logically equivalent to its contrapositive.

Contrapositive: If x≠3, then x ≠ y or y≠3


(ii) Definition of contrapositive: A conditional statement is logically equivalent to its contrapositive.


Contrapositive: If n is not an integer, then it is not a natural number.


(iii) Definition of contrapositive: A conditional statement is logically equivalent to its contrapositive.


Contrapositive: If the triangle is not equilateral, then all three sides of the triangle are not equal.


(iv) Definition of contrapositive: A conditional statement is logically equivalent to its contrapositive.


Contrapositive: if xy is not positive integer, then x or y is not negative integer.


(v) Definition of contrapositive: A conditional statement is logically equivalent to its contrapositive.


Contrapositive: If natural number ‘n’ is not divisible by 2 or 3, then n is not divisible by 6.


(vi) Definition of contrapositive: A conditional statement is logically equivalent to its contrapositive.


Contrapositive: The weather will not be cold, if it does not snow.


(vii) Definition of contrapositive: A conditional statement is logically equivalent to its contrapositive.


Contrapositive: If x2>1 then, x is not a real number such that 0<x<1.


More from this chapter

All 69 →
8

Form the biconditional statement p ↔ q, where

p : A natural number n is odd.


q : Natural number n is not divisible by 2.

 8

Form the biconditional statement p ↔ q, where

p : A triangle is an equilateral triangle.


q : All three sides of a triangle are equal.

 10

Write down the converse of following statements :

(i) If a rectangle ‘R’ is a square, then R is a rhombus.


(ii) If today is Monday, then tomorrow is Tuesday.


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


(iv) 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.


(v) If all three angles of a triangle are equal, then the triangle is equilateral.


(vi) If x : y = 3 : 2, then 2x = 3y.


(vii) If S is a cyclic quadrilateral, then the opposite angles of S are supplementary.


(viii) If x is zero, then x is neither positive nor negative.


(ix) If two triangles are similar, then the ratio of their corresponding sides are equal.

 11

Identify the Quantifiers in the following statements.

(i) There exists a triangle which is not equilateral.


(ii) For all real numbers x and y, xy = yx.


(iii) There exists a real number which is not a rational number.


(iv) For every natural number x, x + 1 is also a natural number.


(v) For all real numbers x with x > 3, x2 is greater than 9.


(vi) There exists a triangle which is not an isosceles triangle


(vii) For all negative integers x, x3 is also a negative integers.


(viii) There exists a statement in above statements which is not true.


(ix) There exists a even prime number other than 2.


(x) There exists a real number x such that x2 + 1 = 0.