Question

What can we say about the sets A and B if we only know that

i) AUB= A?
ii) A B = A?
iii) AnB = B n A?
iv) A B=BA?

Answer 1

We can conclude specific information about sets A and B based on the given statements.

Step-by-step explanation:

In order to answer the question, we will analyze each statement individually:

1. AUB = A means that the union of sets A and B is equal to set A. This implies that set B is a subset of set A.
2. A ∩ B = A means that the intersection of sets A and B is equal to set A. This implies that set A is a subset of set B.
3. AnB = B ∩ A means that the intersection of sets A and B is equal to the intersection of sets B and A.
4. A B = BA means that the concatenation of sets A and B is equal to the concatenation of sets B and A.

Based on these statements, we can conclude the following:

1. If AUB = A, then set B is a subset of set A.
2. If A ∩ B = A, then set A is a subset of set B.
3. If AnB = B ∩ A, then the intersection of sets A and B is the same as the intersection of sets B and A.
4. If A B = BA, then the concatenation of sets A and B is the same as the concatenation of sets B and A.