If `g : [a, b]` on to [a, b] is continous, then show that there is some `c in [a, b]` such that g(c) = c

If A nn B^(c)= phi , show that A sub B .

f is a continuous function in [a,b]; g is a continuous function in [b,c]. A function h(x) is defined as h(x)=f(x) for xϵ[a,b) =g(x) for xϵ(b,c]. If f(b)=g(b), then

Using determinants, show that the following points are collinear (a, b + c),(b,c+a) and (c, a + b)

If A^(c) uu B=U , show that A sub B .

If a,b and c are any three vectors in space, then show that (c+b)xx(c+a)*(c+b+a)= [a b c]

If a, b,c are in G.P, then log a, log b, log c are:

Let f : A rarr B and g : B rarr C be onto functions, show that gof is an onto function.

Show that if A sub B , then C -B sub C -A .

If U = { a, b, c, d, e, f, g, h}, find the complements of the following set : A = {a, b, c}

If A, B, C are angles of triangle ABC and a, b, c are lengths of the sides opposite to A, B, C respectively, then show that : a (sin B - sin C)+ b (sin C- sin A)+c (sin A -sin B)= 0 .