6. Suppose U-{1,2,3,7,11,15), A = {2,4,7) and B ={1,2,4). Which statement below is true.
A is a subset of B
U is a subset of B
B is a subset of A
U is the union of A and B
None of the above statements is true based on the given sets.
pick one anyways
If I have to pick one statement, it would be "B is a subset of A."
To determine which statement is true, we need to understand the definitions of subsets and the union of sets.
1. Subset: A set A is a subset of set B if every element of A is also an element of B. In other words, if every element in A is contained within B.
2. Union: The union of two sets A and B, denoted by A ∪ B, is the set that contains all the elements that are in A or B, or both.
Now, let's evaluate each statement:
A is a subset of B:
To determine whether A is a subset of B, we need to check if every element in A is also in B.
A = {2, 4, 7}, B = {1, 2, 4}
Since every element in A is also in B (2 and 4), the statement "A is a subset of B" is true.
U is a subset of B:
To determine whether U is a subset of B, we need to check if every element in U is also in B.
U = {1, 2, 3, 7, 11, 15}, B = {1, 2, 4}
Since U contains elements that are not in B (3, 7, 11, 15), the statement "U is a subset of B" is false.
B is a subset of A:
To determine whether B is a subset of A, we need to check if every element in B is also in A.
A = {2, 4, 7}, B = {1, 2, 4}
Since all the elements in B are contained within A (2 and 4), the statement "B is a subset of A" is true.
U is the union of A and B:
To determine whether U is the union of A and B, we need to check if U contains all the elements in A and B.
A = {2, 4, 7}, B = {1, 2, 4}
The union of A and B, A ∪ B, is {1, 2, 4, 7}. Since U = {1, 2, 3, 7, 11, 15}, it does not contain all the elements in A and B. Therefore, the statement "U is the union of A and B" is false.
Based on our evaluation:
- The statement "A is a subset of B" is true.
- The statement "U is a subset of B" is false.
- The statement "B is a subset of A" is true.
- The statement "U is the union of A and B" is false.