Ordered of pairs

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I dont know the concept or how to answer the question.

Suppose there are two sets, $X=\{1,2\}$ and $Y=\{a,b\}$.

  • What are all the ordered pairs in the form of (element of $X$, element of $Y$)?
  • What are all the ordered pairs in the form of (element of $Y$, element of $X$)?
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To ask all the ordered pairs in a specific form essentially means you need to present all possible combinations of elements of both sets, $X$ and $Y$, in a specific order. For example, in the first case, we have that all the ordered pairs in that form are $$ (1,a),\,\,(1,b),\,\,(2,a)\,\,\text{and}\,\,(2,b). $$ The second answer is similar. For a more detailed answer please follow the link on the comment regarding the cross product of two sets.