Rewrite the following statement with “if-then” in five different ways conveying the same meaning.

If a natural number is odd, then its square is also odd.

Asked by Pragya Singh | 11 months ago |  103

1 Answer

Solution :-

The given statements can be written in five different ways as follows.

(i) A natural number is odd implies that its square is odd.

(ii) A natural number is odd only if its square is odd.

(iii) If the square of a natural number is not odd, then the natural number is not odd.

(iv) For a natural number to be odd, it is necessary that its square is odd.

(v) For the square of a natural number to be odd, it is sufficient that the numbe is odd.

Answered by Abhisek | 11 months ago

Related Questions

Determine whether the argument used to check the validity of the following statement is correct: p: “If x2 is irrational, then x is rational.” The statement is true because the number x2 = π2 is irrational, therefore x = π is irrational.

Class 11 Maths Mathematical Reasoning View Answer

Which of the following statements are true and which are false? In each case give a valid reason for saying so

(i) p: Each radius of a circle is a chord of the circle.

(ii) q: The centre of a circle bisect each chord of the circle.

(iii) r: Circle is a particular case of an ellipse.

(iv) s: If x and y are integers such that x > y, then – x < – y.

(v) t: \( \sqrt{11}\) is a rational number.

Class 11 Maths Mathematical Reasoning View Answer

By giving a counter example, show that the following statement is not true. p: “If all the angles of a triangle are equal, then the triangle is an obtuse angled triangle.”

Class 11 Maths Mathematical Reasoning View Answer

Show that the following statement is true “The integer n is even if and only if n2 is even”

Class 11 Maths Mathematical Reasoning View Answer

Show that the following statement is true by the method of the contrapositive p: “If x is an integer and x2 is odd, then x is also odd.”

Class 11 Maths Mathematical Reasoning View Answer