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Zorluk: KolaySets, Set Operations, and Venn Diagrams

In a technology conference of 6060 software developers, 3535 write code in Python, 2828 write in Java, and 1212 write in both Python and Java. How many developers write in neither of these two languages?

Cevap: 9 developers

Cevap

The number of developers who write in neither Python nor Java is 99.
The total number of developers writing in at least one language is given by 35+28−12=5135 + 28 - 12 = 51. Subtracting this from the universal set size of 6060 gives 60−51=960 - 51 = 9 developers who write in neither language.

Adım Adım Çözüm

1
Calculate the number of developers who write in at least one of the languages.
n(P∪J)=35+28−12=51n(P \cup J) = 35 + 28 - 12 = 51
By the principle of inclusion-exclusion for two sets, n(P∪J)=n(P)+n(J)−n(P∩J)n(P \cup J) = n(P) + n(J) - n(P \cap J).
2
Subtract from the universal set total to get the complement.
n((P∪J)′)=60−51=9n((P \cup J)') = 60 - 51 = 9
The number of elements outside the union is the universal set total minus the union cardinality.

Anahtar Kavram

Two-set inclusion-exclusion and complement cardinality
Tahmini Süre:1m 0s
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Sets, Set Operations, and Venn Diagrams

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