Let A = {\bullet ,\square, \bigotimes} and B = {\square,\ominus, \bullet}. (a) List the elements of A X B and B X A. The parentheses and comma in an ordered pair are not necessary in cases such as this where the elements of each set are individual symbol.
(b) Identifiy the intersection of A X B and B X A, for the case above, and then guess at a general rule for the intersection of A µ B and B µ A. where A and B are any two sets.

(a) With A = {•, □, ⊗} and B = {□, ⊖, •}, we have

A × B = {(•, □), (•, ⊖), (•, •), (□, □), (□, ⊖), (□, •), (⊗, □), (⊗, ⊖), (⊗, •)}

and

B × A = {(□, •), (□, □), (□, ⊗), (⊖, •), (⊖, □), (⊖, ⊗), (•, •), (•, □), (•, ⊗)}

(b) The intersection of the two sets above is

(A × B) ∩ (B × A) = {(•, •), (•, □), (□, •), (□, □)}

Not sure what µ is supposed to represent, but I suppose you meant to again write × as in the Cartesian product. By definition, for any two sets A and B, we have

A × B = {(a, b) | a ∈ A and b ∈ B}

Then

(A × B) ∩ (B × A) = {(a, b) | a ∈ A ∩ B and b ∈ A ∩ B}

In the product found above, notice that • and □ are both elements of A and B, while ⊗ and ⊖ are exclusive to either set.

pla·gia·rism

/ˈplājəˌrizəm/

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noun

the practice of taking someone else's work or ideas and passing them off as one's own.

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