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GO Classes CS 2025 | Weekly Quiz 4 | Set Theory | Question: 6

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Let $S$ be an infinite set and $S_1 \dots , S_n$ be sets such that $S_1 \cup S_2 \cup \dots \cup S_n = S$. Then
  1. at least one of the sets $S_i$ is a finite set
  2. not more than one of the sets $S_i$ can be finite
  3. at least one of the sets $S_i$ is an infinite
  4. None of the above
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2 Answers

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5 votes

Source: https://gateoverflow.in/2301/gate-cse-1993-question-8-3 

$\color{red}{\text{Finite Union of Finite Sets is Finite.}}$ i.e. If we have finite number of finite sets, then their union will necessarily be finite.

Union of $S_1,S_2, \dots, S_n$ is infinite set $\text{iff}$ at least one $S_1,S_2, \dots, S_n$ is infinite set.

Find Detailed Video Solution with time stamp here: https://youtu.be/mOfUwNN2JP8?si=NW9OQEbs5D3XxS2Y&t=2302

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