What can you say about sets A and B if you know that.
1)A U B = A?
2)A n B = A?
3)A - B = A?
Is B an empty set?
@ bobpursley no the question did not specify
To understand the relations between sets A and B based on the given conditions, let's break down each condition and explain what it implies:
1) A U B = A
This condition states that the union of sets A and B is equal to A. In other words, every element in A is also an element in B. To determine the relationship between A and B based on this condition, we can conclude that B is a subset of A. Additionally, we can say that A is equal to the union of A and the empty set (∅). This is because if B is a subset of A and the union of A and the empty set (∅) includes all elements in A, then A U ∅ = A.
2) A n B = A
This condition states that the intersection of sets A and B is equal to A. In other words, every element in A belongs to B as well. From this condition, we can infer that A must be a subset of B. Additionally, based on this condition, we can say that if B is a superset of A, then the intersection of A and B is equal to A, as all elements in A are also elements in B.
3) A - B = A
This condition states that the set difference between A and B (i.e., the elements that are in A but not in B) is equal to A. From this condition, we can conclude that B must be the empty set (∅), as if B had any elements, the set difference A - B would not be equal to A. In other words, every element in A must also be in B for A - B to be equal to A.
In summary:
1) A U B = A implies that B is a subset of A.
2) A n B = A implies that A is a subset of B.
3) A - B = A implies that B is the empty set (∅).