Problem 25 - Algebra and Trigonometry

Question

Find the intersection of the sets. $$\\{1,3,5,7\\} \cap\\{2,4,6,8,10\\}$$

Step-by-Step Solution

Answer

The intersection of the sets \(\{1,3,5,7\}\) and \(\{2,4,6,8,10\}\) is \(\{\}\).

Step 1: Understand the Sets

First, examine the given sets. The two given sets are \(\{1,3,5,7\}\) and \(\{2,4,6,8,10\}\). The first set consists of odd numbers and the second set consists of even numbers.

Step 2: Identify Common Elements

Next, identify which elements are common to both sets. An examination of these sets shows that they are disjoint – there are no elements that are part of both sets.

Step 3: Write the Intersection Set

Since the two sets have no common elements, the intersection set is the empty set, or \(\{\}\).