Question

binary operations - BTech entrance mathematics question.​

Answer 1

Answer:

$\boxed{\boxed{\huge\pink{{(b) \: \: 0}}}}$

Step-by-step explanation:

Given----> A binary operation

x0 y = x+y + xy , for all x, y € X

To find ----> Value of identity element

Concept used----> If e is the identity element of binary operation then

x 0 e = x = e 0 x , for all x € X

$Soluion\longrightarrow \\We \: know \: that \\ xoy \: = x + y + xy \\ Now \\ x \: o \: 0 \: = x + 0 + x \: (0) \\ \: \: \: \: \: \: \: \: \: \: \: = x + 0 + 0 \\ \: \: \: \: \: \: \: \: \: \: \: = x$

$Now \\ 0 \: o \: x \: = 0 + x + 0 \: (x) \\ \: \: \: \: \: \: \: \: \: \: \: = 0 + x + 0 \\ \: \: \: \: \: \: \: \: \: \: \: = x \\ So \\ x \: o \: 0 \: \: = 0 \: o \: x \: = \: x$

$So \: 0 \: is \: the \: identity \: element \: of \: operation$

Answer 2

Answer:

Given----> A binary operation

x0 y = x+y + xy , for all x, y € X

To find ----> Value of identity element

Concept used----> If e is the identity element of binary operation then

x 0 e = x = e 0 x , for all x € X

We know that,

x o y=x+y+xy

Now

xo0 =x+0+x(0)

=x+0+0

=x

Now,

0ox=0+x+0(x)

=0+x+0

=xSoxo0

=0ox=x