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  • Write down the contrapositive of the following statements: (i) If x = y and y = 3, then x = 3.

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.

Answers (1)

(i) Contrapositive definition: A conditional statement is said to be logically equivalent to its contrapositive.

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

(ii) Contrapositive definition: A conditional statement is said to be logically equivalent to its contrapositive.

Thus, Contrapositive: If n is not an integer, then it is not a natural no.

(iii) Contrapositive definition: A conditional statement is said to be logically equivalent to its contrapositive.

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

(iv) Contrapositive definition: A conditional statement is said to be logically equivalent to its contrapositive.

Thus, Contrapositive: If xy is not a positive integer, then either x or y is not a negative integer.

(v) Contrapositive definition: A conditional statement is said to be logically equivalent to its contrapositive.

Thus, Contrapositive: If natural no. ‘n’ is not divisible by 2 or 3, then n is not divisible by 6.

(vi) Contrapositive definition: A conditional statement is said to be logically equivalent to its contrapositive.

Thus, Contrapositive: The weather will not be cold if it doesn’t snow.

(vii) Contrapositive definition: A conditional statement is said to be logically equivalent to its contrapositive.

Thus, Contrapositive: If x^{2} > 1 then, x is not a real number such that 0 < x < 1.

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