Total Property Solutions

This article is about total property solutions. Total property solution is nothing but it is some properties which helps to solve some math problems. There are different math properties we use in different chapters of mathematics. With the help of the total property solution we can complete many different problems. Tutor vista is the best website to help with total property solutions. There will be online tutors in these websites to help the students anytime about the different topics in mathematics. Below we can see some total property solutions.


Total Property Solutions

Here we can work total property solutions under the topic of binary operations.

Closure property

An operation * on a nonempty set S is said to satisfy the closure property, if

a in S, b in S rArr  a*b in S for all a, b in S

Also, in this case, we say that S is closed for *.

An operation * on a nonempty set S, satisfying the closure property is known as a binary operation

Properties of a binary operation

(i) Associative law : A binary operation * on a non empty set S is said to be associative, if

(a*b)*c = a*(b*c) for all a,b,c in S

(ii) Commutative law   A binary operation * on a nonempty set S is said to be commutative if

a*b = b*a for all a, b in S

(iii) Distributive Law   Let * and . be two binary operations on a nonempty set S. We say that * is distributive over(.), if

a*(b.c) = (a*b).(a*c) for all a, b, c in S
Total Property Solutions

Here we see some example using of total property solutions

Example 1: (i) Addition on the set N of all natural numbers is a binary operation, since

a in N, b in N rArr a+b in N for all a,b in N

(ii) Multiplication on N is a binary operation, since

a in N, b in N rArr a x b in N for all a,b in N

Similarly, addition as well as multiplication is a binary operation on each one of the sets Z, Q, R and C of integers, rationals, reals and comples numbers respectively.

Example 2 : Let R be the set of all real numbers. Then,

(i) Addition on R satisfies the closure property, the associative law and the commutative law,

(ii) Multiplication on R satisfies the closure property, the associative law and the commutative law,

(iii) Multiplication distributes addition on R, since

a. (b+c) = a.b+a.c for all a, b, c in R