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.

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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 8.3 years ago by

teamques10 ★ 69k

modified 3.2 years ago by

pedsangini276 • 4.8k

Mumbai University > Computer Engineering > Sem 3 > Discrete Structures

Marks: 4 Marks

Year: Dec 2013

discrete mathematics

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written 8.3 years ago by

teamques10 ★ 69k

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) …

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