Final answer:
The solution set of the intersection between the sets {xl x<-5} and {xl x>5} is the empty set, as no real number can be both less than -5 and greater than 5 at the same time.
Step-by-step explanation:
The question asks about the solution set of the intersection between two sets: {xl x<-5} and {xl x>5}. To solve this, we need to understand the definition of set intersection and the meaning of the inequalities given for the sets.
The set {xl x<-5} includes all real numbers that are less than -5. Whereas, the set {xl x>5} includes all real numbers that are greater than 5. The intersection of these two sets, denoted by \( \x \cap \x \), would be the set of all numbers that are simultaneously less than -5 and greater than 5.
However, no real number can satisfy both conditions at the same time. A number cannot be less than -5 and greater than 5. Therefore, the intersection of these two sets is the empty set, represented by \(\emptyset\). Hence, the correct answer to the question is option c, the empty set.