Question

State, with a reason, the given statement is true or false .
{ α1, α2, ...., αn } is a set only if all the αis
follow a given rule.

Answer 1

Answer on Question #80367 – Math – Abstract Algebra

Question

$\{\alpha_{1}, \alpha_{2}, \ldots, \alpha_{n}\}$ is a set only if all the $\alpha_{i}$ follow a given rule. Is this statement TRUE or FALSE? Give a reason for your answer.

Solution

False. A set can be defined in different ways. A set is not always defined by a rule. On the other hand, if a set is defined by a list of objects, a rule can be introduced and the set can be redefined. Objects $\alpha_{1}, \alpha_{2}, \ldots, \alpha_{n}$ can be thought as rule variables or as list elements.

The correct reason varies according to how sets are introduced and how $\alpha_{1}, \alpha_{2}, \ldots, \alpha_{n}$ are named.

Answer: False.

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