Let R be a relation such that R={(a ,c), (c ,g) ,(d ,e), (d, f) ,(g, f)} then `(RoR^(-1))^(-1)` is

Let R be a relation such that R={(a d) (c g) (d e) (d f) (g f)} then (ROR^(1))^(-1) is

Let R be a relation such that R={(a d) (c g) ) (d e) (d f) (g f)} then (R R^(-1))^(-1) is {(d d) (g g) (e e) (f f) (e f) (f e)} {(e a) (f a) (f c)} {(a e) (a f) (c f) {(d d) (g g) (e e) (f f) (e f)}

Let R be a relation such that R={(a d) (c g) (d e) (d f) (g f)} then (R@R^(-1))^(-1) is qquad {(d d) (g g) (e e) (f f) (e f) (f e)} O{(e a) (f a) (f c)} O{(a e) (a f) (c f) O{(d d) (g g) (e e) (f f) (e f)}

Let R be a relation such that R={(a d) (c g) (d e) (d f) (g f)} then (R@R^(-1))^(-1) is qquad {(d d) (g g) (e e) (f f) (e f) (f e)} O{(e a) (f a) (f c)} O{(a e) (a f) (c f) O{(d d) (g g) (e e) (f f) (e f)}

Let R be a relation on NxxN defined by (a , b) R(c , d)hArra+d=b+c for a l l (a , b),(c , d) in NxxN show that: (i) (a , b)R (a , b) for a l l (a , b) in NxxN (ii) (a , b)R(c , d)=>(c , d)R(a , b)for a l l (a , b), (c , d) in NxxN (iii) (a , b)R (c , d)a n d (c , d)R(e ,f)=>(a , b)R(e ,f) for all (a , b), (c , d), (e ,f) in NxxN

Let R be a relation over the set NxxN and it is defined by (a,b)R(c,d)impliesa+d=b+c . Then R is

If A B C and D E F are two triangles such that (A B)/(D E)=(B C)/(E F)=(C A)/(F D)=2/5 , then A r e a( A B C): A r e a( D E F)= 2:5 (b) 4: 25 (c) 4: 15 (d) 8: 125

(d) Let f:R rarr R be a differentiable bijective function.Suppose g is the inverse function of f such that G(x)=x^(2)g(x). If f(2)=1 and f'(2)=(1)/(2) , then find G'(1) .

Let f and g be differentiable on [0,1] such that f(0)=2,g(0),f(1)=6 and g(1)=2. Show that there exists c in(0,1) such that f'(c)=2g'(c)