Let f be a function from A to B. Let S and T be subsets of B. Show that a) f^(-1)(S∪T) = f^(-1)(S) ∪ f^(-1)(T).
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Step 1
Let x be an element of f^(-1)(S∪T). This means that f(x) is in S∪T. So, f(x) is in S or f(x) is in T. If f(x) is in S, then x is in f^(-1)(S). If f(x) is in T, then x is in f^(-1)(T). Therefore, in either case, x is in f^(-1)(S) ∪ f^(-1)(T). So, we have shown Show more…
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