Consider f: A→B and let S, T ⊆ A. 1. Prove: f(S∩T)⊆f(S)∩f(T) 2. Draw a diagram that shows why this is a subset relationship and not set equality. In other words, show why there can be elements in f(S)∩f(T) that are not in f(S∩T). 3. How can f be limited so that equality occurs. In other words, how do you eliminate the problem in your drawing? 4. Which step in your proof is not reversible?

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