Ask
Login
0
812views
If f:$A \rightarrow B$ be both one-to-one and onto, the prove that $f^{-1}: B \rightarrow A$ is also both one-to-one and onto.
written 7.4 years ago by gravatar for teamques10 teamques10 ★ 65k modified 2.3 years ago by gravatar for pedsangini276 pedsangini276 • 4.8k

Mumbai University > Computer Engineering > Sem 3 > Discrete Structures

Marks: 4 Marks

Year: Dec 2013
discrete mathematics
ADD COMMENT EDIT
1 Answer
0
2views
written 7.4 years ago by gravatar for teamques10 teamques10 ★ 65k

f is one to one and onto hence $$a_1, a_2 € A \\ f(a_1)=f(a_2)-\gt a_1=a_2 \\ b € B a € A$$

s.t. b =f(a)

To prove that $f^{-1}$ is one one onto.

Let $f (a_1) = b_1 \ \ \ and \ \ \ f (a_2) = b_2$

$$f^{-1}(b_1) …

Create a free account to keep reading this post.

and 5 others joined a min ago.

ADD COMMENT EDIT
Please log in to add an answer.