Now here are some questions for you to try to answer In each

Now, here are some questions for you to try to answer. In each case, try to figure out as much as you can. Justify your answers with proofs and counterexamples.

1) Suppose W and X are subsets of A

Solution

a) Always true.

f(WUX) =f(W) Uf(X)

W= (a,b) X = (b,c,d)

WUX = (a,b,c,d)

f(w) = {f(a), f(b)} and f(X) = {f(b) , f(c), f(d)}

f(W)Uf(X) = {f(a), f(b),f(c), f(d)} = f(WUX)

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b) True always

W\\X is the set of all elements in W and not in X

Or W\\X = W-WX

So f(W-WX) = f(W)\\f(X)

c) True