Function

Consider an arbitrary function f:X→Y. It includes two important set mappings. If A is a subset of X, then its image f(A) is the subset of Y defined by f(A)={f(x) : x ε A}. Similarly, if B is a subset of Y, then its inverse image f^-1(B) is a subset of X defined by f^-1(B)={x : f(x) ε B }.

1. Which of the following is not true?

a) A_{1}\subseteq A_{2} \Rightarrow f(A_{1})\subseteq f(A_{2})

b) f\left( \bigcap_{i=1}^{n}{A_{i}}\right) =\bigcap_{i=1}^{n}{f(A_{i}})

c) f\left( \bigcup_{i=1}^{n}{A_{i}}\right) =\bigcup_{i=1}^{n}{f(A_{i}})

d) f(A)\subseteq f(A^{c}) iff f is onto where A_{i}\subset X

2. Which of the following is not true?

a) A=f^{-1}(f(A))

b) f^{-1}(Y)=X

c) f^{-1}(\cup_{i}B_{i} )=\cup_{i}f^{-1}(B_{i})

d) f^{-1}(\cap_{i}B_{i} )=\cap_{i}f^{-1}(B_{i}) \: where \: B_{i}\subset Y

Most of the time goes in understanding what these freaking symbols mean over here. Please a detailed solution of what is happening here would be great.

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