Home
Class 12
MATHS
Define ** on Z by a ** b=a+b +1 AA a, b ...

Define `**` on Z by `a ** b=a+b +1 AA a, b in Z`. Then the identity element of z is

A

1

B

0

C

2

D

`-1`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • DISCRETE MATHEMATICS

    SURA PUBLICATION|Exercise FILL IN THE BLANKS|10 Videos

  • DISCRETE MATHEMATICS

    SURA PUBLICATION|Exercise CHOOSE THE INCORRECT STATEMENT:|5 Videos

  • DISCRETE MATHEMATICS

    SURA PUBLICATION|Exercise GOVERNMENT EXAM QUESTIONS|2 Videos

  • DIFFERENTIALS AND PARTIAL DERIVATIVES

    SURA PUBLICATION|Exercise 5 MARKS|4 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    SURA PUBLICATION|Exercise ADDITIONAL QUESTIONS ( 5 MARKS)|6 Videos

Similar Questions

Explore conceptually related problems

Let Z denote the set of all integers and A = { (a,b) : a^2 +3b^2 = 28 ,a,b in Z } and B= {(a,b ):a gt b, in Z} . Then the number of elements in A nn B is

In (z, **) where ** is defined by a ** b=a^b , prove that ** is not a binary operation on z.

On Z, define ox by (m ox n) = m^(n) + n^(m) : AA m, n in Z . Is ox binary on Z?

Let Z be the set of all integers and R be the relation on Z defined as R={(a , b); a ,\ b\ in Z , and (a-b) is divisible by 5.} . Prove that R is an equivalence relation.

Let R be the relation on Z defined by R= {(a,b): a, b in Z, a-b "is an integer"). Find the domain and range of R.

If w=alpha+ibeta, where beta!=0 and z!=1 , satisfies the condition that ((w- barw z)/(1-z)) is a purely real, then the set of values of z is |z|=1,z!=2 (b) |z|=1a n dz!=1 z= z (d) None of these

Let f be a subset of Z xx Z defined by f ={ (ab ,a+b) : a,b in Z } is f a function from z to Z ? Jusity your answer

Let f be the subset of Z xx Z defined by f={(ab,a+b) : a,b in Z} . Is f a function from Z to Z? Justify your answer.

In (z, **) where ** is defined as a ** b = a +b +2 . Verify the commutative and associative axiom.