Question

Construct the appropriate number sets with the given information. Use the sets to match the following:

Given:

a = 0
b = B
c = A∪B=B
d = A
e = A∩B=B
If A⊂B, then:
A. c
B. a
C. e
D. d

Answer 1

Using set theory, we've determined that option C, e, correctly matches the condition given that A is a subset of B (A⊂B) because e represents the intersection of A and B (A∩B), which will just be A if A is a subset of B.

Step-by-step explanation:

The question requires constructing appropriate number sets and using them to match the given variables based on the operations within set theory. Given the information a = 0 (which lacks context and may be a typo, so we will disregard it), b = B, c = A∪B, d = A, and e = A∩B, with the additional fact that A is a subset of B (A⊂B), we can infer the following:

• Since A⊂B, all elements of A are also elements of B.
• The set A∩B, which is the intersection of A and B, would contain elements that are in both A and B. Given that A is a subset of B, A∩B will just be A.
• The set A∪B, which is the union of A and B, would contain all elements that are either in A or in B. Since A is a subset of B, A∪B will just be B.

Therefore, if A⊂B, then:
A. c is not the correct match since c represents A∪B, which is equal to B, not A.
B. a cannot be determined from the given information (a = 0 is not relevant to the set operations described).
C. e is the correct match since e represents A∩B, which, given that A⊂B, would be the set A.
D. d is also not the correct match as d is simply A and does not add any additional information regarding the relationship to B in this context.