On `RR-{1}`, a binary operation `**` is defined by `a**b=a+b-ab` Statement - I: Every element of `RR-{1}` is inveritble Statement -II: o is the identity element for * on `RR-{1}`.
A
Statement -I is True Statement -II is True , Statement -II is a correct explanation for Statement -I
B
Statement -I is True. Statement -II is True, Statement -II is not a correct explanition for Statement -I
A binary operation @ on QQ-{1} is defined by a**b=a+b-ab for all a,binQQ-{1}. Prove that every element of QQ-{1} is invertible.
Let ** be a binary operation on set QQ-{1} defined by a**b=a+b-abinQQ-{1}. e is the identity element with respect to ** on QQ . Every element of QQ-{1} is invertible, then value of e and inverse of an element a are---
If the binary operation ** on the set ZZ is defined by a**b=a+b-5 , then the identity element with respect to ** is K . Find the value of K .
Show that the binary operation ** defined on RR by a**b=ab+2 is commutative but not associative.
Let * be a binary operations on Z and is defined by , a * b = a + b + 1, a, bin Z . Find the identity element.
Let A={0,1,2,3,4,5} be a given set, a binary operation @ is defined on A by a@b=ab(mod6) for all a,bin A. Find the identity element for @ in A . Show that 1 and 5 are the only invetible elements in A.
An operation @ on QQ-{-1} is defined by a@b=a+b+ab for a,binQQ-{-1}. Find the identity element einQQ-{-1} .
Let * be a binary operation defined by a* b = L.C.M , (a,b) AA a,b in N . Show that the binary operation * defined on N is commutative and associative. Also find its identity element of N.
A binary operation @ is defined on RR-{-1} by a@b=a+b+ab for all a,binRR-{-1}. (i) Discuss the commutativity and associativity of @ on RR-{-1} . Find the identity element, if exists. (iii) Prove that every element of RR-{-1} is invertible.
A binary operation ** is defined on the set RR_(0) for all non- zero real numbers as a**b=(ab)/(3) for all a,binRR_(0), find the identity element in RR_(0) .
CHHAYA PUBLICATION-BINARY OPERATION-Assertion-Reason Type
