Set Membership
Try some of the problems below for determining whether a particular element belongs to each given set!
Try the following!
True!
Notice that 3 is listed second in \(\{1,3,5,7,11\}\), and so is in the set.
False!
4 is not listed anywhere in the set \(\{1,3,5,2,11\}\)
True!
When you see a pattern in the set, it is helpful to fill in the “…” with the elements that come next. Doing so in \(\{1,3, 5, …, 15, 17, 19, 21\}\) gives you \(\{1,3,5,7,11,13,15,17,19, 21\}\). As you can tell, 7 is in this set!
True!
There isn’t really a limitation as to what can be contained in a set. This means you can have sets within sets, or sets as elements of bigger sets. In the case of \(\{1,3, 5, 7, \{1,2\}, \{3,4,5\}\}\), there are 6 elements inside this set, NOT 9. The sets \(\{1,2\}\) and \(\{3,4,5\}\) as a whole are elements of the bigger set. Therefore, \(\{1,2\}\in \{1,3, 5, 7, \{1,2\}, \{3,4,5\}\}\).
False!
While the set \(\{2,3,4,5,\{1,5\}\}\) contains the elements 2 and 5, it does not contain the SET CONTAINING 2 and 5; i.e. \(\{2,5\}\notin \{2,3,4,5,\{1,5\}\}\).
True!
The interval \((2,10)\) consists of all numbers (including decimals and fractions) between 2 and 10, but not including 2 and 10. 3 is definitely a number that falls between 2 and 10.
True!
\(3.14159\) is a number between \(-1\) and \(5\).
True!
The interval \([2.52,4)\) contains all numbers (including decimals and fractions) between 2.52 and 4, including 2.52, but NOT including 4.
True!
The interval \([-20,\infty)\) includes all numbers greater than or equal to -20. 13 is definitely greater than or equal to -20 and therefore lives in that interval.
False!
The interval \((-\infty, 12)\) includes only numbers STRICTLY less than 12 (as indicated by the round bracket at 12). Since 12 isn’t STRICTLY less than itself, 12 isn’t in the interval.