CameraIcon

SearchIcon

MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Binary Operation

An equation ...

Question

An equation $$ on $Z^{+}$ (the set of all non-negative integers) is defined as $a b = a - b, \forall a, b \in Z^{+}$ . Is $*$ a binary operation on $Z^{+}$ ?

Open in App

Solution

Operation $$ is defined as $a b = a - b$ , $\forall a, b \in Z^{+}$
$a, b \in Z^{+}$ But, if $b > a$ then $a - b$ becomes negative.
So, it is not true that $a - b \in Z^{+} \forall a, b \in Z^{+}$
Thus, $a * b$ does not belong to $Z^{+}$
Hence, $*$ is not binary on $Z^{+}$

Suggest Corrections

thumbs-up

1

Similar questions

Q. 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 of this.
(i) On Z⁺, defined * by a * b = a − b
(ii) On Z⁺, defined * by a * b = ab
(iii) On R, define by a*b = ab²
(iv) On Z⁺ define * by a * b = |a − b|
(v) On Z⁺, define * by a * b = a
(vi) On R, define * by a * b = a + 4b²
Here, Z⁺ denotes the set of all non-negative integers.

Q. On the set Z of integers a binary operation * is defined by a * b = ab + 1 for all a , b ∈ Z. Prove that * is not associative on Z.

Q. On the set Z of all integers a binary operation * is defined by a * b = a + b + 2 for all a, b ∈ Z. Write the inverse of 4.

Q. On Z, the set of all integers, a binary operation * is defined by a * b = a + 3b − 4. Prove that * is neither commutative nor associative on Z.

Let * be an operation on Z be defined on Z as a* b = a^b for all a,b ϵ Z. Then which one of these options is correct?

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Binary Operations

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Binary Operation

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon