Is {11, 14} not a subset of {11, 12, 13, 14, ...}?
Understand the Problem
The question is asking us to determine if {11, 14} is not a subset of {11, 12, 13, 14, ...}. We need to evaluate whether the first set is entirely contained within the second set to determine if the (\nsubseteq) relation is true or false.
Answer
False
Answer for screen readers
False
Steps to Solve
- Identify the sets
We have two sets: $A = {11, 14}$ and $B = {11, 12, 13, 14, ...}$.
- Determine if A is a subset of B
Check if every element in set $A$ is also in set $B$. $11$ is in $B$, and $14$ is in $B$. Therefore, $A$ is a subset of $B$. We can write this as $A \subseteq B$.
- Evaluate the $\nsubseteq$ relation
The question uses the "not a subset of" symbol ($\nsubseteq$). Since $A$ is a subset of $B$, the statement $A \nsubseteq B$ is false.
False
More Information
The set $B = {11, 12, 13, 14, ...}$ represents all integers from 11 to infinity. Any set containing elements that are between 11 and infinity will be a subset of $B$
Tips
A common mistake is to misinterpret the "not a subset of" ($\nsubseteq$) symbol. Remember that $A \nsubseteq B$ is true only if there is at least one element in $A$ that is not in $B$.
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