Question: only the question 4 please! Exercise III Consider sets A, B, C, and functions f : A - B and g : B - C.

only the question 4 please!

only the question 4 please! Exercise III Consider sets A, B, C,

Exercise III Consider sets A, B, C, and functions f : A - B and g : B - C. 1. Show that if gof is 1-1, then f is 1-1. 2. Show that if go f is onto, then g is onto. 3. Consider two functions u : A - C and v : C - A. Assume that vou = idA and uov = idc. Show that u is a bijection and that v = u-1. Use Questions 1 and 2. 4. Assume that f and g are bijective. Show that go f is bijective and that (go f)-1 = f-log-1. Use Question 3

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!