Problem 34 - Algebra and Trigonometry

Question

Find the union of the sets. $$\\{e, m, p, t, y\\} \cup \varnothing$$

Step-by-Step Solution

Answer

The union of the sets \(\{e, m, p, t, y\}\) and \(\varnothing\) is the set \(\{e, m, p, t, y\}\).

Step 1: Identify the sets

The two sets in consideration are the set \(\{e,m,p,t,y\}\) and the null set \(\varnothing\).

Step 2: Understand the union operation

A union of two sets includes all the unique elements present in both the sets. In this case since one of the sets is a null set, meaning it does not have any elements, the result of a union operation will be the set itself.

Step 3: Apply the union operation

Applying the union operation to the two sets, we get that the union of set \(\{e, m, p, t, y\}\) and the null set \(\varnothing\) will be the set \(\{e, m, p, t, y\}\). The null set did not contribute any new elements to the union as it has no elements.