Define Reflexive. Give one example.

2

(a)

Define symmetric Relation. Give one example

2

(a)

Define Transitive Relation. Give one example.

2

(a)

Consider the relation perpendicular on a set  of lines in a plane. Show that this relation is symmetric and neither reflexive and nor transitive.

2

(a)

What is meant by one-one function?

2

(a)

\(f(x)=x^{ 2 },x\in R\) Find \(\frac { f(1.1)-f(1) }{ 1.1-1 } \)

2

(a)

Find whether the following operations are binary operation or not
(i) * On N defined by a * b = a^b 
(ii) * On Z  defined by a*b = a^b 

2

(a)

Let * be a binary operation on the set R defined by a*b = a + b + ab, a, b \(\in R\) Solve the equation 2*(3*x) = 33

2

(a)

If the binary operation * on the set of integers Z is defined by a*b = 3a + b² then find the value of
(i) 4*3
(ii) 5*2

2

(a)