Which of the following is not true?

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Rational numbers are closed under addition

Rational numbers are closed under subtraction

Rational numbers are closed under multiplication

Rational numbers are closed under division

answer is D.

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Detailed Solution

We need to find the false statement.
Rational numbers are not closed under division.
Except for division, all of these operations, addition, subtraction, multiplication, result in closed rational numbers.
i.e.
If

a, b

are two rational numbers, then

a + b, a - b, a \times b

are also rational number.
But

a \div b

is not always a rational number because

\frac{1}{0}

is not defined but 1 and 0 are rational numbers.
Hence, the statement that rational numbers are closed under division is not true.
Thus, option 4 is correct.

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