Practice question · Multiple choice
For A = {1, 2}, the statement "{1} is a subset of A" is true while "{1} is an element of A" is false. Why does putting braces around the 1 change which relation holds?
Hints
- List A's elements explicitly. Is {1} one of the things on that list?
- Subset is about what is INSIDE; element is about what A directly contains.
Show the answer
D. Because A's elements are 1 and 2, not sets, and {1} is a set.
Why
A contains exactly two things, the numbers 1 and 2, and {1} is neither, but every member of {1} lies in A, which is what subset means. The distinction becomes unmistakable with A = {1, {1}}, where {1} is both, for different reasons. Set theory builds everything by nesting, so containing and being-among-your-members must stay apart.
Practise Sets and Set-Builder Notation
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