If A = {1,2,3} and f,g are relations corresponding to the subset \(A\times A\) indicated against them, which of f,g is a function? why?
f = {(1, 3) (2, 3), (3, 2)}; g = {(1, 2), (1, 3), (3, 1)}.

3

(a)

Let A = {0,1, 2, 3} and define a relation R on A as follows:
R = {(0, 0), (0, 1), (0, 3), (1, 0), (1, 1), (2, 2), (3, 0), (3, 3)}. Is R Reflexive? Symmetric? Transitive?

3

(a)

If f = {(5, 2), (6, 3)}, g = {(2, 5), (3, 6)}, write fog.

3

(a)

Let f : \(R\rightarrow R\) be defined by \(f(X)=X^{ 2 }+1\) Find the pre-image of
(i) 17
(ii) -3.

3

(a)

Let the function f:\(R\rightarrow R\) to be defined by:
\(f(x)=cosx\) for all \(x\in R\).
Show that 'f' is neither one-one nor onto.

3

(a)