The question in Hindi can be translated as follows:

Given sets $A = \{1, 2\}$ and $B = \{a, b, c\}$, find the total number of relations from $A$ to $B$.

To solve this, let's analyze the problem step-by-step.

Solution:

1. The total number of relations from a set $A$ to a set $B$ is the number of possible subsets of $A \times B$.
2. The Cartesian product $A \times B$ represents all possible ordered pairs where the first element is from $A$ and the second is from $B$.

Since:

• $A = \{1, 2\}$ (which has 2 elements)
• $B = \{a, b, c\}$ (which has 3 elements)

The Cartesian product $A \times B$ will have $2 \times 3 = 6$ elements: $A \times B = \{(1, a), (1, b), (1, c), (2, a), (2, b), (2, c)\}$

3. Each element in $A \times B$ can either be included in a relation or not, meaning we have 2 choices (include or exclude) for each of the 6 pairs.
4. Therefore, the total number of possible relations from $A$ to $B$ is $2^6 = 64$.

Answer:

The total number of relations from $A$ to $B$ is $\boxed{64}$.

Would you like more details on Cartesian products or relations? Here are some related questions you might find helpful:

1. What is the Cartesian product of two sets and how is it calculated?
2. How do you determine the number of subsets of a given set?
3. What is the difference between a function and a relation?
4. How does the size of set $B$ affect the total number of relations from $A$ to $B$?
5. Can a relation exist without any ordered pairs?

Tip: Remember, the number of possible relations from set $A$ to set $B$ is based on the number of elements in the Cartesian product $A \times B$. Each pair in $A \times B$ can independently either be included in or excluded from a relation, giving $2^{\text{number of pairs}}$.