Explore BrainMass

# Set Theory: Surjective and Bijective

Not what you're looking for? Search our solutions OR ask your own Custom question.

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

i) If A is countable and f: A=>B is surjective, show that B is countable.
ii). Show that a function f: A=>B is bijective if, and only if, there is a function g: B=>A
with gf = 1_A and fg = 1_B.
iii) If f: A=>B, g: B=>C and h: C=>D are functions show that h(gf) = (hg)f.
iv) Let f: A=>B and g: B=>C be functions.
a) Show that if f is surjective and gf injective then g is injective.
b) Is it possible for gf to be injective when g is not? Explain.
v) Show that if A has n elements then P(A) has 2^n elements, for all n real numbers of N.

https://brainmass.com/math/discrete-math/set-theory-surjective-bijective-503115

#### Solution Preview

Please see the attached document for full solutions.

(i) If A is countable, then we ...

#### Solution Summary

We solve several problems in set theory. Surjective and bijectives are examined.

\$2.49