Math, asked by A5H35, 10 months ago

*
The binary operation'*' defined on the set of integer as a*b= |a+b|+5 is

Commutative
Non commutative
Associative but Non commutative
Associative​

Answers

Answered by jayanthivijayakumar0
3

in mathematics, a binary operation is commutative if changing the order of the operands does not change the result. It is a fundamental property of many binary operations, and many mathematical proofs depend on it.

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Answered by parulsehgal06
0

In the given options correct option is not mentioned. Please refer to the detailed solution and correct option.

Answer:

The given condition a*b=|a+b|+5 satisfies both Associative law and Commutative law.

Step-by-step explanation:

Binary operation:

Binary operation means when a mathematical operation is performed on any two elements of a set, then the output also belongs to the same set.

The binary operation can be of the form *, +, -

Associative law:

Let a, b, c ∈ Z(set of integers) with binary operation '*' then Associative law is defined as  a*(b*c)=(a*b)*c        

Commutative law:

Let a,b ∈ Z(set of integers) with binary operation '*' then Commutative law is defined as   a*b = b*a

  • Given a*b=|a+b|+5 and * is defined on the set of integers.

        Now we have to check whether the above-given condition

         satisfies the laws or not.

  • For a, b, c ∈ Z, a*b=|a+b|+5
  • Now check   a*(b*c)=(a*b)*c

           Consider

L.H.S = a*(b*c) = a*(|b+c|+5)

                       = a*(b+c+5)

                       = |a+b+c+5|+5

                       = a+b+c+10

R.H.S = (a*b)*c = (|a+b|+5)*c

                       = (a+b+5)*c

                       = |a+b+5+c|+5

                       = a+b+c+5+5

                       = a+b+c+10

Since, L.H.S = R.H.S

So, the given condition satisfies Associative law.

  • For a, b ∈ Z, a*b=|a+b|+5
  • Check a*b = b*a

Consider

L.H.S= a*b = |a+b|+5

                 = a+b+5

R.H.S = b*a = |b+a|+5

                   = b+a+5  ( Since a, b ∈ Z, a+b = b+a)

Since L.H.S = R.H.S

So, the given condition satisfies Commutative law.

Hence the given condition a*b=|a+b|+5 satisfies both Associative law and Commutative law.

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