Home
Class 12
MATHS
Let A = N×N and ⋅ be the binary operatio...

Let A = N×N and ⋅ be the binary operation on A defined by(a, b) ∗(c, d) = (a + c, b + d) . Show that ⋅ is commutative and associative. Find the identity element for ⋅ on A, if any.

Text Solution

Verified by Experts

Given `A:N×N` with binary operation * definrd by `(a,b)∗(c,d)=(a+c,c+d).`
Step:1-Checking if the operation is commutative:
An opertion ∗ on A is commutative if
`a∗b=b∗a∀a,bϵA`
...
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    NCERT|Exercise EXERCISE 1.2|12 Videos

  • RELATIONS AND FUNCTIONS

    NCERT|Exercise Exercise 1.1|16 Videos

  • RELATIONS AND FUNCTIONS

    NCERT|Exercise SOLVED EXAMPLES|50 Videos

  • PROBABILITY

    NCERT|Exercise EXERCISE 13.2|18 Videos

  • SETS

    NCERT|Exercise EXERCISE 1.3|1 Videos

Similar Questions

Explore conceptually related problems

Let A = N xx N and ** be the binary opertation on A defined by (a, b) ** (c, d) = (a+c, b+d) . Show that ** is commutative and associative.

Let A=RR and * be the binary operation on A defined by (a,b)*(c,d)=(a+c,b+d). show that is commutative and associative.Find the identity element for * on A.

Let * be a binary operation on Z defined by a*b=a+b-4 for all a,b in Z. show that * is both commutative and associative.

Let '**' be a binary operation defined on NxxN by : (a, b)**(c, d)=(a+c,b+d) . Prove that '**' is commutative and associative.

Let Q be the set of all rational numbers and let ** be a binary operation on QxxQ defined by (a,b)**(c,d)=(ac,b+ad). Determine whether ** is commutative and associative. Find the identity element for ** and invertible elements of QxxQ. Or Let f:[0,oo) toR be a function defined by f(x) =9x^(2)+6x-5. Prove that f is not invertible. modify only the condomin of f to make f invertible and then find its inverse.

Let R_(0) denote the set of all non-zero real numbers and let A=R_(0)xx R_(0) .If * is a binary operation on A defined by (a,b)*(c,d)=(ac,bd) for all (a,b),(c,d)in A* show that * is both commutative and associative on A( ii) Find the identity element in A

Let '**' be a binary operation on Q defined by : a**b=(2ab)/(3) . Show that '**' is commutative as well as associative.

Let * be a binary operation on N defined by a*b = a^(b) for all a,b in N show that * is neither commutative nor associative

Let Q_(0) be the set of all nonzero reational numbers Let * be a binary operation on Q_(0) defined by a*b = (ab)/(4) for all a,b in Q_(0) (i) Show that * is commutative and associative (ii) Find the identity element in Q_(0) (iii) Find the inverse of an element a in Q_(0)

Let A=NxNa n d^(prime)*' be a binaryoperation on A defined by (a , b)*(C , d)=(a c , b d) for all a , b , c , d , in Ndot Show that '*' is commutative and associative binary operation on A.

Home
Profile