Mathematics

Mathematics

Problem

Suppose U=ZU = \mathbb{Z} , C={y∈Z∣−4≤y≤−1}C = \{y \in \mathbb{Z} \mid -4 \le y \le -1\} , and D={y∈Z∣−7≤y<0}D = \{y \in \mathbb{Z} \mid -7 \le y < 0\} . a. List CC and DD . b. Find C∩DC \cap D . c. Find C∪DC \cup D . d. Show that n(C∪D)=n(C)+n(D)−n(C∩D)n(C \cup D) = n(C) + n(D) - n(C \cap D) .
Intuitive explanation

This problem is about understanding set complements and operations on finite sets of integers. The key insight is to first explicitly list out what CC and DD contain—they're just integers in specific ranges—then use the definitions of complement and set operations (like union or intersection) relative to the universal set U=ZU = \mathbb{Z}. Once you see the actual elements, the relationships become clear.

Intuitive explanation

This problem is about understanding set complements and operations on finite sets of integers. The key insight is to first explicitly list out what CC and DD contain—they're just integers in specific ranges—then use the definitions of complement and set operations (like union or intersection) relative to the universal set U=ZU = \mathbb{Z}. Once you see the actual elements, the relationships become clear.

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