To determine which of the options is a subset of the given set {1, 3, 5, 7, 9, 135, 27}, we need to understand what a subset is. A subset is a set where all its elements are also contained in another set.
For example, if we consider the set {1, 3, 5}, every element (1, 3, and 5) is included in the larger set {1, 3, 5, 7, 9, 135, 27}. Thus, {1, 3, 5} is a subset of the larger set.
Now, let’s check the following options and see which, if any, are subsets:
- {1, 3}
- {1, 10}
- {27, 9}
- {135, 5}
The sets {1, 3} and {27, 9} each have their members present in the original set, so they qualify as subsets. Meanwhile, {1, 10} includes 10, which is not in the original set, making it not a subset. Lastly, {135, 5} is also a subset of the original set.
In conclusion, the correct answers are {1, 3}, {27, 9}, and {135, 5} as they are all subsets of the original set.