"Is smaller than" over the set of eggs in a box isa)Transitive...
If a is smaller than b and b is smaller than c , then a is definitely smaller than c.
hence it is transitive
"Is smaller than" over the set of eggs in a box isa)Transitive...
Transitive (T)
Transitivity is a property of relations that states that if a relation holds between two elements, and it also holds between the second element and a third element, then it must also hold between the first element and the third element.
Explanation:
To determine if the relation "smaller than" over the set of eggs in a box is transitive, we need to consider whether the property holds for any three elements in the set.
Let's consider three eggs in the box: A, B, and C.
If egg A is smaller than egg B, and egg B is smaller than egg C, then we need to determine if it is true that egg A is smaller than egg C.
Example:
Let's assume that egg A is smaller than egg B, and egg B is smaller than egg C.
A < />
B < />
If we compare egg A and egg C, we need to check if it holds that egg A is smaller than egg C.
If both egg A and egg B are smaller than egg C, then it is true that egg A is smaller than egg C.
A < b="" />< />
In this case, the relation "smaller than" over the set of eggs in a box is transitive because the property holds for any three elements in the set.
Conclusion:
Therefore, the correct answer is option 'A', transitive (T). The relation "smaller than" over the set of eggs in a box satisfies the transitive property.
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