Which of the following binary operation is not commutative-Addition-Multiplication-Subtraction-None of these-

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Cummutative Law of Binary Operation

Which of the ...

Question

Which of the following binary operation is not commutative?

Addition

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Multiplication

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Subtraction

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None of these

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Solution

The correct option is C
Subtraction

For a binary operation $^{}$ to be commutative, we need a $^{}$ b = b $^{*}$ a for all a and b.

For multiplication and addition, this is true because ab = ba and a+b = b+a. But for subtraction a-b is not equal to b-a for all a and b. So it's not commutative.

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Similar questions

Q. Which of the following is true?
(a) * defined by

a * b = \frac{a + b}{2}

is a binary operation on Z
(b) * defined by

a * b = \frac{a + b}{2}

is a binary operation on Q
(c) all binary commutative operations are associative
(d) subtraction is a binary operation on N

Show that addition, subtraction, and multiplication are binary operations on $R$ , but division is not a binary operation on $R$ . Further, show that division is a binary operation on the set $R_{*}$ of nonzero real numbers.

Q. Show that addition and multiplication are associative binary operation on

R

. But subtraction is not associative on

R

. Division is not associative on

R_{*}

Show that subtraction are not binary operation on natural number N

Identity of the binary operation subtraction is 0

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Which of the following binary operation is not commutative?

The correct option is C Subtraction For a binary operation ∗ to be commutative, we need a ∗ b = b ∗ a for all a and b. For multiplication and addition, this is true because ab = ba and a+b = b+a. But for subtraction a-b is not equal to b-a for all a and b. So it's not commutative.

The correct option is C
Subtraction

For a binary operation $^{}$ to be commutative, we need a $^{}$ b = b $^{*}$ a for all a and b.

For multiplication and addition, this is true because ab = ba and a+b = b+a. But for subtraction a-b is not equal to b-a for all a and b. So it's not commutative.