How many relations can be formed from a set with 3 elements?

How many relations can be formed from a set with 3 elements?

Correct Answer: 512

Step 1: Understand what a set is. A set is a collection of distinct objects. In this case, we have a set with 3 elements.
Step 2: Identify the number of elements in the set. Here, n = 3.
Step 3: Know the formula for the number of relations on a set. The formula is 2^(n^2).
Step 4: Calculate n^2. Since n = 3, we calculate 3^2, which equals 9.
Step 5: Substitute n^2 into the formula. We now have 2^(3^2) = 2^9.
Step 6: Calculate 2^9. This equals 512.
Step 7: Conclude that the number of relations that can be formed from a set with 3 elements is 512.

Relations in Set Theory – A relation on a set is a subset of the Cartesian product of the set with itself. The number of possible relations is determined by the number of subsets of this Cartesian product.
Power Set – The number of relations corresponds to the number of subsets of the Cartesian product, which is calculated as 2 raised to the power of the size of the Cartesian product.
Cartesian Product – The Cartesian product of a set with n elements results in n^2 ordered pairs, which is crucial for determining the number of relations.