Problem $1.$ Suppose we have two sets, $A=\{5,10\},$

and $1n3$

and $1n3$

and $1n10$ is universal set.

$(1)$ Write down what is the element of $B,C,U$ respectively.

$(2)$ Find $AB$

$(3)$ Find $D=(AB{)}^{\text{'}}.$

$(4)$ Find $AB.$

Problem $2.$ Consider a coffee dataset collected by Grind Co Coffee roaster to decide their recipe. They

collected from an experiment measuring three attributes: roast level $(9$ means darkest, $0$ means lightest$),$

aroma intensity $($higher the more intensive$),$ and bean size $($in mm $).$ Each attribute is described and rounded

by a natural number.

$(1)$ Given an experiment measure that is described by the three attributes above, write the concise Cartesian

product set in the format of element $|$ condition