Question

6. The expression axb
=bxa represents the
following property of
rational numbers
*​

Answer 1

Answer:

Step-by-step explanation:

A*B = B*A.

This represents commutative property of multiplication.

Answer 2

Answer:

Natural numbers (N): The counting numbers {1, 2, 3, …}, are called natural numbers. Some authors include 0, so that the natural numbers are {0, 1, 2, 3, …}.

Whole numbers(W): The numbers {0, 1, 2, 3, …}.

Integers (Z): Positive and negative counting numbers, as well as zero:{…, -2, -1, 0, 1, 2,…}.

Rational numbers (Q): Numbers that can be expressed as a ratio of an integer to a non-zero integer. All integers are rational, but the converse is not true.

Real numbers (R): Numbers that have decimal representations that have a finite or infinite sequence of digits to the right of the decimal point. All rational numbers are real, but the converse is not true.

For all natural numbers m, n and p the following hold.

m + n = n + m                        (Commutative property of addition)

m + (n + p) = (m + n) + p     (Associative property of addition)

m x n = n x m               (Commutative property of multiplication)

m x (n x p) = (m x n) x p       (Associative property of multiplication)

m x (n + p) = (m x n) + (m x p)               (distributive property)

 

Every non-empty subset of natural numbers of N (or W) has the smallest element.

This is called the well ordering property of natural numbers.

Step-by-step explanation:We know, the set of all Positive and negative counting numbers, as well as zero:{…, -2, -1, 0, 1, 2,…}. is called whole numbers. Denoted by Z. If m and n are two whole numbers, with the extension of addition and multiplication, we have to following properties:

Closure property: for all integers a, b, both a + b and b + a also integers;

Commutative property: for all integers a, b

a + b = b + a

a x b = b x a

Associative property: for all integers a, b, c

a + (b + c) = (a + b) + c

a x (b x c) = (a x b) x c

Distributive property: for all integers a, b, c

a x (b + c) = (a x b) + (a x c)

Cancellation law: if a, b, c are integers such that, c ≠ 0 and ac = bc

Then a = b.

so a*b=b*a shows Commutative property of multiplication