Home
Class 12
MATHS
On the set Z of integers, if the binar...

On the set `Z` of integers, if the binary operation * is defined by a*b=`a+b+2` , then find the identity element.

A

commutative

B

associative

C

commutative and associative

D

none of above

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercies 1e|10 Videos

  • RELATIONS AND FUNCTIONS

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 1.1|8 Videos

  • RELATIONS AND FUNCTIONS

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercies 1c|9 Videos

  • PROBABIILITY

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|19 Videos

  • THREE-DIMENSIONAL GEOMETRY

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|23 Videos

Similar Questions

Explore conceptually related problems

If the binary operation * on the set Z is defined by a*b =a+b-5, then find the identity element with respect to *.

If the binary operation . on the set Z is defined by a.b =a+b-5, then find the identity element with respect to ..

For the binary operation * on Z defined by a*b= a+b+1 the identity element is

Let * be a binary operation o Q defined by a*b= (ab)/4 for all a,b in Q ,find identity element in Q

Define a binary operation on a set.

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

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

On Q, the set of all rational numbers, a binary operation * is defined by a*b=(a b)/5 for all a , b in Qdot Find the identity element for * in Q. Also, prove that every non-zero element of Q is invertible.

On Q, the set of all rational numbers, a binary operation * is defined by a*b=(a b)/5 for all a , b in Qdot Find the identity element for * in Q. Also, prove that every non-zero element of Q is invertible.

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 Zdot