Which of the following is not true; a) Rational numbers are closed under addition. b) Rational numbers are closed under subtraction. c) Rational numbers are closed under multiplication. d) Rational numbers are closed under division.
Answers
Answer:
option D. Rational numbers are not closed under division.
Step-by-step explanation:
In any of the properties like closure, commutative, associative and distributive property division does not satisfy a
or not closed under division. (not defined)
RATIONAL NUMBERS
(d) Rational numbers are closed under division is not true.
GETTING TO KNOW MORE ABOUT RATIONAL NUMBERS:
* Rational numbers, when combined with addition and multiplication, provide an integer-containing field that may be found in any field holding integers.
* In other words, the field of rational numbers is a prime field, and a field has characteristic zero if and only if it has a subfield of rational numbers. Algebraic number fields are finite extensions of Q, and the algebraic closure of Q is the field of algebraic numbers.
* The rational numbers are a dense subset of the real numbers in mathematical analysis. Using Cauchy sequences, Dedekind cuts, or infinite decimals, the real numbers can be created from the rational numbers.