 # Write down the contrapositive `
Question:

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 x 2 < 1.

Solution:

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

We know that a conditional statement is logically equivalent to its contrapositive.

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

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

We know that a conditional statement is logically equivalent to its contrapositive.

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

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

We know that 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) If x and y are negative integers, then xy is positive.

Solution:

We know that a conditional statement is logically equivalent to its contrapositive.

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

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

We know that 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) If it snows, then the weather will be cold.

We know that a conditional statement is logically equivalent to its contrapositive.

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

(vii) If x is a real number such that 0 < x < 1, then x 2 < 1.

We know that a conditional statement is logically equivalent to its contrapositive.

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