I was given a question that asks "Let A={1,2} ,B={x,3,y},C={2,y}. Find A x B x C and C x B x C " I have an example that I could go by but i'm not sure what they were multiplying together to get it. If someone could explain that it would help a lot!
TIA
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$\begingroup$You have sets of ordered triples.
For example, $$A\times B\times C = \{ (1,x,2), (1,x,y), (1,3,2),..., (2,y,y)\}$$
Note that in $A\times B\times C$ the first coordinate comes from $A$, the second comes from $B$ and the third comes from $C$.
Similarly, $$C\times B \times C = \{ (2,x,2), (2,3,2),...,(y,y,y)\}$$
where the first coordinate comes from $C$, the second comes from $B$ and the third comes from $C$.
$\endgroup$ 4 $\begingroup$For sets $A,B,C$, the cartesian product $A\times B\times C$ is defined as $$A\times B\times C = \{(a,b,c)\;|\; a\in A,\;b\in B,\;c\in C\}$$In english, this means that its the set of all triples where the first element comes from $A$, the second from $B$, and the third from $C$.
In your example, $$A\times B\times C =$$$$ \{(1,x,2),(1,x,y),(1,3,2),(1,3,y),(1,y,2),(1,y,y),(2,x,2),(2,x,y),(2,3,2),(2,3,y),(2,y,2),(2,y,y)\}$$
Try evaluating $C\times B\times C$ in a similar manner, replacing the elements of $A$ with those of $C$.
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