Question

How can we define X∪Y mathematically?

A) { a :a ∈ X but a ∉ Y}
B) {a:a ∈ U but a ∉ X}
C) {a: a ∈ X or a ∈ Y}
D) {a:a ∈ Y and a ∈ X}

Answer 1

The union of sets X and Y, denoted as X∪Y, includes all elements that are in either set X or set Y, or in both. The correct definition is {a: a ∈ X or a ∈ Y}, which corresponds to Option C.

Step-by-step explanation:

The mathematical definition of the union represented by X∪Y is best described as the set of elements that belong to either set X or set Y, including those that are in both. Therefore, the correct mathematical definition for X∪Y is Option C: {a: a ∈ X or a ∈ Y}. This means that if an element is in set X, set Y, or in both sets, it is a part of the union of X and Y.

For instance, using the given reference information, if we consider A AND B, the outcome is the intersection of A and B, resulting in the set {14,16,18}. However, A OR B represents the union of the two sets, which includes all the distinct elements from both sets, resulting in the set {2, 4, 6, 8, 10, 12, 14, 15, 16, 17, 18, 19}. The notion 'A AND B' is parallel to the intersection of two sets (a common set of elements) in contrast to 'A OR B', which exemplifies the union of the two sets, mirroring X∪Y.