Amalgamation generally refers to the process of combining multiple entities into a single entity. We need to identify which equation captures this idea of merging multiple parts into one unified whole.
Here are the given equations:
1. [tex]\( A + B + C = A \)[/tex]
2. [tex]\( A + B + C \ A + B + C \)[/tex]
3. [tex]\( A + B + C = D \)[/tex]
4. [tex]\( A + B + C = A + D \)[/tex]
Let's analyze each equation step-by-step:
1. [tex]\( A + B + C = A \)[/tex]
In this equation, it states that the sum of [tex]\( A \)[/tex], [tex]\( B \)[/tex], and [tex]\( C \)[/tex] results in [tex]\( A \)[/tex]. This implies that both [tex]\( B \)[/tex] and [tex]\( C \)[/tex] are zero, which contradicts the general idea of amalgamation where all entities contribute to form a new entity.
2. [tex]\( A + B + C \ A + B + C \)[/tex]
This is not a valid mathematical equation because there is no operator or equality sign connecting the two parts. Therefore, it doesn’t represent amalgamation or any other standard mathematical concept.
3. [tex]\( A + B + C = D \)[/tex]
This equation suggests that [tex]\( A \)[/tex], [tex]\( B \)[/tex], and [tex]\( C \)[/tex] combine to form a new entity [tex]\( D \)[/tex]. This is consistent with the concept of amalgamation, where different elements are combined to create something new.
4. [tex]\( A + B + C = A + D \)[/tex]
This equation implies that the combination of [tex]\( A \)[/tex], [tex]\( B \)[/tex], and [tex]\( C \)[/tex] results in something that retains [tex]\( A \)[/tex] and adds [tex]\( D \)[/tex]. This does not align with the idea of amalgamation as it suggests retaining [tex]\( A \)[/tex] and creating [tex]\( D \)[/tex] from [tex]\( B \)[/tex] and [tex]\( C \)[/tex], rather than forming one single new entity from all the parts.
The equation that best represents the idea of amalgamation, where multiple entities are combined to form a single new entity, is:
[tex]\( A + B + C = D \)[/tex]
Therefore, the correct answer is:
3. [tex]\( A + B + C = D \)[/tex]
