$+$ is

binary operation on

R

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not a binary operation on

R

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a binary operation in

Q^{c}

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not a binary operation in

E

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Solution

The correct option is B binary operation on $R$
Addition is a binary operation on R since it satisfies the following properties:
It is closed in R, i.e; sum of two real numbers is also real.
It follows Commutativity and Associativity.
Existence of Identity element 0, which when added to a number gives back the same number.
Existence of Additive Inverse. The negative of a number added to that number gives the identity element 0.

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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

Q. Which of the following is not a binary operation on

R

Q. Examine whether the operation

*

defined on

R

a * b = a b + 1

is
(i) a binary or not.
(ii) if a binary operation, is it associative or not ?

Let * be any binary operation on the set R defined by a * b = a + b – ab, then the binary operation * is

Determine whether or not each of the definition of $*$ given below gives a binary operation. In the event that $*$ is not a binary operation, give justification for this.
(iii) On R, defined $*$ by $a * b = a b^{2}$

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