Question

Let U= {1,2,3,4,5,6,7,8,9} , X= {8,7,6}, Y= {8,9,7} , and Z= {8,5,6}

a Find X ∪ Y.
b Find Y ∪ X.
c Make a conjecture.

Answer 1

The union of sets X and Y, denoted by X ∪ Y or Y ∪ X, is {6, 7, 8, 9}. This demonstrates that the union operation for sets is commutative.

Step-by-step explanation:

To find the union of sets X and Y, we combine all the unique elements from both sets without repetition. Therefore, X ∪ Y, which means X union Y, is the set of all elements that are in X, or Y, or in both. To perform this operation, we list all the distinct elements from both sets.

• Set X = {8, 7, 6}
• Set Y = {8, 9, 7}

The union of X and Y is {6, 7, 8, 9}. Note that even though the number 8 and 7 appear in both sets, they are only listed once in the union.

Similarly, Y ∪ X is the union of Y and X. Since union is a commutative operation, Y ∪ X will have the same elements as X ∪ Y, resulting again in {6, 7, 8, 9}.

In conclusion, the conjecture that can be made here is that the union operation is commutative, meaning that X ∪ Y = Y ∪ X regardless of the order in which the sets are listed.