I know the sideways U means "is a subset of" and if there is a line under it, it means "is equal to"
I have two sets:
{-3,0,3} _____ {-3,-1,1,3}
choose the correct symbol
a. sideways U with line under it and slash through it
b. sideways U with line under it but no slash at all
-3, and 3 are subsets, but 0 is not in the other set... would that make the answer b?
please, help?
thank you!
As you said, 0 is not in the second set,
So, the answer is (a): NOT a subset
To determine the correct symbol to use, we need to assess if the first set {-3, 0, 3} is a subset of the second set {-3, -1, 1, 3}.
By definition, a set A is considered a subset of set B if all elements of A are also elements of B. In this case, if every element in the first set is also present in the second set, then the first set is a subset of the second set.
Let's check each element in the first set and see if it is present in the second set:
- The element -3 is present in the second set {-3, -1, 1, 3}.
- The element 0 is not present in the second set.
- The element 3 is present in the second set.
Since not all elements of the first set are present in the second set, we can conclude that the first set {-3, 0, 3} is not a subset of the second set {-3, -1, 1, 3}.
Therefore, the correct symbol to use is the sideways U with a line under it but no slash. This symbol indicates a subset relationship without an equality.
So, in this case, the correct symbol would be b. sideways U with a line under it but no slash at all.
The correct symbol to choose in this case would be option B: sideways U with a line under it but no slash.
The symbol "is a subset of" (∈) is used when every element in the first set is also an element in the second set. In this case, {-3, 0, 3} is a subset of {-3, -1, 1, 3} because all the elements in the first set are also present in the second set.
It is important to note that the symbol for "is equal to" (=) is not applicable here because the two sets are not exactly the same. Even though {-3, 3} are subsets, the element 0 does not appear in the second set. Therefore, option B is the correct choice.