Let Two sets are called disjoint if there Difference is the empty setGroup startsTrue or FalseTrue, unselectedFalse, unselected

Answering the Question

1. Understanding Disjoint Sets: Two sets $A$ and $B$ are called disjoint if they have no elements in common, which mathematically can be expressed as: $A \cap B = \emptyset$ Here, $A \cap B$ denotes the intersection of sets $A$ and $B$, and $\emptyset$ represents the empty set.

2. Your Question: The statement in question is whether two sets are called disjoint if their difference is the empty set. The difference of two sets $A$ and $B$ is defined as: $A - B = \{ x \in A \, | \, x \notin B \}$

3. Analyzing the Statement: If the difference $A - B$ is the empty set, it implies that every element of $A$ is also in $B$ (i.e., $A \subseteq B$). Therefore, the statement does not hold true because it defines sets that are not disjoint.

4. Final Verification: Since the definition of disjoint sets requires the intersection to be empty, and if the difference is empty, it means one set entirely contained in another. Thus, the statement is False.

Final Answer

False: Two sets are called disjoint if their intersection is the empty set, not their difference.