Q10 of 18 Page 13

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.


Given statement is: "If a natural number is odd, then its square is also odd"

Identical five statements are:

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

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

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

More from this chapter

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8
Check whether the following pair of statements is negation of each other. Give reasons for your answer.

(i) x + y = y + x is true for every real number x and y.

(ii) There exists a real number x and y for which x + y = y + x.

9
State whether the "OR" used in the following statements is "exclusive" or "inclusive". Give reasons for your answer.

(i) Sun rises or moon sets.

(ii) To apply for a driving license, you should have a ration card or a passport.

(iii) A lady gives birth to a baby boy or baby girl.

(iv) All integers are positive or negative.

11
Write the contra positive and converse of the following statements.

(i) If x is a prime number, then x is odd.

(ii) If the two lines are parallel, then they do not intersect in the same plane.

(iii) Something is cold implies that it has low temperature.

(iv) You cannot comprehend geometry if you do not know how to reason deductively.

(v) x is an even number implies that x is divisible by 4

12
Write each of the following statements in the form of "if-then"

(i) You get a job implies that your credentials are good.

(ii) The Banana tree will bloom if it stays warm for a month.

(iii) A quadrilateral is a parallelogram if its diagonals bisect each other.

(iv) To get an A+ in the class, it is necessary that you do all the exercises of the book.