State whether the following statements are true or false:

(a) The set of all even natural numbers is a infinite set.

(b) Every non-empty subset of has the smallest element.

(c) Every integer can be identified with a rational number.

(d) For each rational number, one can find the next rational number.

(e)There is no largest rational number.

(f) Every integer is either even or odd.

(g) Between any two rational numbers, there is an integer.

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Solution

(a) The set of all even natural numbers is an infinite set.

Thus, the given statement is FALSE.

(b) Every non-empty subset of natural numbers has the smallest element.

Thus, the given statement is FALSE.

(c) Let n be an integer. It can be written in the form of a rational number as.

Thus, the given statement is TRUE.

(d) For any rational number, we cannot find the next rational number.

Thus, the given statement is FALSE.

(e)There is no largest rational number.

Thus, the given statement is FALSE.

(f)The set of integers is a collection of all even and odd numbers.

Thus, the given statement is TRUE.

(g) Between any two rational numbers, there are infinite rational numbers.

Thus, the given statement is FALSE.

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Similar questions

State whether the following statements are true or false. Give reasons for your answer.

(i) Every natural number is a whole number.

(ii) Every whole number is a natural number.

(iii) Every integer is a whole number.

(iv) Every integer is a rational number.

(v) Every rational number is an integer.

(vi) Every rational number is a whole number.

\frac{a}{b}

\frac{a}{b} = \frac{a \times m}{b \times m}

\frac{2}{3} is equal to \frac{4}{6} .

Question 49

State whether the given statement is True or False.

Every integer is a rational number but every rational number need not be an integer.

(i) Every natural number is a rational number.

(ii) Every integer is a rational number.

(iii) 0 is a whole number, but not a rational number.

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