Question

Read the following statements carefully: Statement:1 Rational numbers are closed under multiplication. Statement ll: Rational numbers are closed under division. *​

Answer 1

Answer:

"closed"

Rational number is not closed under division

Explanation:

The rational numbers are "closed" under addition, subtraction, and multiplication. Under division, we run into the problem of division by 0, which makes the statement that "the rationals are closed under division" false. ... Irrational numbers are "not closed" under addition, subtraction, multiplication or division.

Rational number is not closed under division. ... Irrational numbers are not closed under addition, subtraction, multiplication or division.

Answer 2

Statement I is correct

Statement II is incorrect.

• Closure property states that when a set of numbers is closed under any arithmetic operation such as addition, subtraction, multiplication, and division and is performed on any two numbers of the set with the answer being another number from the set itself.
• A rational number is a number that is expressed as the ratio of two integers, where the denominator should not be equal to zero.
• When multiplication operation is done on two rational numbers, the output is always a rational number. Hence, rational numbers are closed under multiplication.
• The product of two rational numbers is always a rational number.
• But rational numbers are not closed under division.
• The division of two rational numbers is not always a rational number.
• For example, division by zero gives an undefined number.

#SPJ3