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Zorluk: ZorLogical Venn Diagrams

In a district administration department, a survey was conducted among 250250 officers regarding their technical expertise in three digital governance domains: Cyber Security (CC), Data Analytics (DD), and Public Grievance Portals (PP). The data collected is as follows:
- 120120 officers have expertise in Data Analytics.
- 115115 officers have expertise in Cyber Security.
- 100100 officers have expertise in Public Grievance Portals.
- 5050 officers have expertise in both Data Analytics and Cyber Security.
- 4545 officers have expertise in both Cyber Security and Public Grievance Portals.
- 4040 officers have expertise in both Data Analytics and Public Grievance Portals.
- 2020 officers possess expertise in all three digital governance domains.

Based on the given data, how many officers have expertise in EXACTLY TWO of these three domains?

Cevap: 75 officers

Cevap

The total number of officers who have expertise in exactly two digital governance domains is 75.
To find the number of officers with expertise in exactly two domains, we calculate the exclusive intersection regions by subtracting the central three-set intersection (2020) from each of the given double-intersection totals: (50−20)+(45−20)+(40−20)=30+25+20=75(50 - 20) + (45 - 20) + (40 - 20) = 30 + 25 + 20 = 75.

Adım Adım Çözüm

1
Calculate the number of officers in the region representing expertise in ONLY Data Analytics and Cyber Security
50−20=3050 - 20 = 30 officers
The total intersection of Data Analytics and Cyber Security includes officers proficient in all three domains. Subtracting the 3-domain count isolates those proficient in only these two.
2
Calculate the number of officers in the region representing expertise in ONLY Cyber Security and Public Grievance Portals
45−20=2545 - 20 = 25 officers
Subtracting the 3-domain count from the total intersection of Cyber Security and Public Grievance Portals isolates those proficient in only these two.
3
Calculate the number of officers in the region representing expertise in ONLY Data Analytics and Public Grievance Portals
40−20=2040 - 20 = 20 officers
Subtracting the 3-domain count from the total intersection of Data Analytics and Public Grievance Portals isolates those proficient in only these two.
4
Sum the three mutually exclusive regions representing expertise in exactly two domains
30+25+20=7530 + 25 + 20 = 75 officers
Adding these disjoint sets yields the total number of officers with expertise in exactly two of the three digital governance domains.

Anahtar Kavram

Principle of Inclusion-Exclusion and Venn Diagram Region Partitioning
Tahmini Süre:2m 0s
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Konular

Logical Venn Diagrams

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