Q. 95.0( 1 Vote )

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.

Answer :

(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.


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