Question

Answer true or false. $$ \{2\} \in \mathcal{P}(\{1,2\}) $$

   Answer true or false.
$$
\{2\} \in \mathcal{P}(\{1,2\})
$$

Discrete Mathematics

Discrete Mathematics

Richard Johnsonbaugh 8th Edition

Chapter 1, Problem 92

Instant Answer

Solved by Expert Manisha Sarker

10/08/2022

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The power set of a set is the set of all possible subsets of the set. Show more…

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Answer true or false. $$ \{2\} \in \mathcal{P}(\{1,2\}) $$

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Key Concepts

Subset

A subset is a set where every element in the subset is also an element of another set. The concept is fundamental in set theory and is used to compare two sets, where one is completely contained within the other. It is important to note the difference between an element and a subset, as an element is a single item within a set, whereas a subset is a set composed of elements from another set.

Power Set

The power set of a set is the set of all possible subsets, including the empty set and the set itself. It encapsulates every combination of elements that can be formed from the original set, making it a central concept in set theory. The power set is instrumental in exploring relationships between sets, particularly in understanding the structure and properties of subsets.

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