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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 $x y$ is positive.
(v) If natural number $\mathrm{n}$ is divisible by 6 , then $\mathrm{n}$ is divisible by 2 and 3 .
(vi) If it snows, then the weather will be cold.
(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 $x y$ is positive.
(v) If natural number $\mathrm{n}$ is divisible by 6 , then $\mathrm{n}$ is divisible by 2 and 3 .
(vi) If it snows, then the weather will be cold.
Solution:
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Verified Answer
(i) If $x \neq 3$ then $x \neq y$ or $y \neq 3$
(ii) If $n$ is not an integer then it is not a natural number.
(iii) If the triangle is not equilateral then all three sides of the triangle are not equal.
(iv) If $\mathrm{xy}$ is not positive integer then either $\mathrm{x}$ or $\mathrm{y}$ is not negative integer.
(v) If natural number $\mathrm{n}$ is not divisible by 2 and 3 then $\mathrm{n}$ is not divisible by 6 .
(vi) The weather will not be cold if it does not snow.
(ii) If $n$ is not an integer then it is not a natural number.
(iii) If the triangle is not equilateral then all three sides of the triangle are not equal.
(iv) If $\mathrm{xy}$ is not positive integer then either $\mathrm{x}$ or $\mathrm{y}$ is not negative integer.
(v) If natural number $\mathrm{n}$ is not divisible by 2 and 3 then $\mathrm{n}$ is not divisible by 6 .
(vi) The weather will not be cold if it does not snow.
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