Question

1.Which of the following statements is false ?
(a) Natural numbers are closed under addition
(b) Whole numbers are closed under addition
(c) Integers are closed under addition
(d) Rational numbers are not closed under addition.

2.Which of the following statements is false ?
(a) Natural numbers are closed under subtraction
(b) Whole numbers are not closed under subtraction
(c) Integers are closed under subtraction
(d) Rational numbers are closed under subtraction.

3.Which of the following statements is true ?
(a) Natural numbers are closed under multiplication
(b) Whole numbers are not closed under multiplication
(c) Integers are not closed under multiplication
(d) Rational numbers are not closed under multiplication.

4.Which of the following statements is false ?
(a) Natural numbers are commutative for addition
(b) Whole numbers are commutative for addition
(c) Integers are not commutative for addition
(d) Rational numbers are commutative for addition.

5.Which of the following statements is true ?
(a) Natural numbers are associative for subtraction
(b) Whole numbers are not associative for subtraction
(c) Integers are associative for subtraction
(d) Rational numbers are associative for subtraction.​

Answer 1

Answer:

1.(D)

2.(A)

3.(A)

4.(C)

5.(A)

Step-by-step explanation:

1. As Rational numbers ARE closed under addition.

2. As Natural numbers ARE closed under subtraction.

3. As Natural numbers are NOT closed under multiplication.

4.As Integers ARE commutative for addition.

5.As Natural numbers are associative for subtraction.

Answer 2

Concept:

A number is closed under addition and multiplication. This can be understood as adding or multiplying two natural numbers results in a natural number.

Associative property can be defined as:

(A + B) + C = A + (B + C)  or (A × B) × C = A × (B × C).

Given:

The statements regarding natural numbers, whole numbers, integers, and rational numbers are given.

Find:

We have to state which of the following statements are true.

Solution:

(1) The following option which is false is Rational numbers are not closed under addition.

A rational number when added to a rational number, the number is a rational number. So, rational numbers are closed under addition.

Hence, Option (d) is the correct answer.

(2) The following option which is false is Natural numbers are closed under subtraction.

When a natural number is subtracted from another natural number there is a chance that the number will be an integer.

Hence, Option (a) is the correct answer.

(3) The following option which is true is Natural numbers are closed under multiplication.

When a natural number is multiplied by another natural number, the number is a natural number. So, Natural numbers are closed under multiplication.

Hence, Option (a) is the correct answer.

(4) The following option which is false is Integers are not commutative for addition.

As integers are closed under addition. They are commutative for addition. So, Integers are commutative for addition.

Hence, Option (c) is the correct answer.

(5) The following option which is true is Whole numbers are not associative for subtraction.

As whole numbers are not closed under subtraction. They are not associative for subtraction. So, Whole numbers are not associative for subtraction.

Hence, Option (b) is the correct answer.

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