Question

Analyze the set below and answer the question that follows. (KUM) n (KUL) Which Venn diagram has shading that represents the given set?

Answer 1

Choice A. The shading in the Venn Diagram shown in the first attachment represents the set
`(K \cup M) \; \cap \; (K \cup L)`.

Explanation:

Let
`A`,
`B`, and
`C` be sets. By the distributive law of sets,
`A \cup (B \cap C)` and
`(A \cup B) \cap (A \cup C)` refer to the same set.

Apply this property to simplify the given expression:

`\begin{aligned}(K \cup M) \; \cap\; (K \cap L) = K\cup (M \cap L)\end{aligned}`

`M \cap L` refers to the intersection between the two lower circles. The union of that intersection with set
`K` (the upper circle) would be the shaded region seen in choice A.