Home General Which operations is the following set closed under?

Which operations is the following set closed under?

Which operations is the following set closed under?

Answer Expert Verified Answer: The answer is addition and multiplication. Step-by-step explanation: Closure property states that – for any numbers ‘a’ and ‘b’ belonging to a set A, if a*b also belongs to set A, then set A is said to be closed under the operation *.

Which of the following set is closed under numerical multiplication?

Let a, b ∈ N then a × b = ab ∈ N. Hence, Natural numbers are closed under multiplication. Hence, Integers are closed under multiplication.

Which of the following set is closed under addition subtraction and multiplication?

The set of rational numbers is closed under addition, subtraction, multiplication, and division (division by zero is not defined) because if you complete any of these operations on rational numbers, the solution is always a rational number Page 8 11.

How do you determine if a set is closed under multiplication?

A set is closed under (scalar) multiplication if you can multiply any two elements, and the result is still a number in the set. For instance, the set {1,−1} is closed under multiplication but not addition.

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What is subtraction of whole numbers?

Subtracting whole numbers is the inverse operation of adding whole numbers. With subtraction, instead of adding two numbers to get a sum, you are removing one number from another to get a difference.

How do you borrow with subtraction?

Borrowing is a two-step process:

  1. Subtract 1 from the top number in the column directly to the left. Cross out the number you’re borrowing from, subtract 1, and write the answer above the number you crossed out.
  2. Add 10 to the top number in the column you were working in.

When you subtract two whole numbers you always get a whole number?

Whole numbers are not a closed set under subtraction: if you subtract two whole numbers, you do not always get a whole number. For example, 2 – 5 = -3 and -3 is not a whole number.

Is the quotient of two whole numbers a whole number?

This is not always true with differences or quotients of natural numbers. The sum or product of two whole numbers is also a whole number, but the difference or quotient of two whole numbers is not always a whole number.

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How do you subtract a number in thousands?

To do this, subtract 1 from the digit in the tens place, and add 10 to the digit in the ones place. Make sure you cross out the original digits and write the new numbers after borrowing.