Question

A = {Tom, Jim, Ann, Kim} B = {Tom, Jim, Ann, Kim} Tom, Jim, Ann are siblings, and Kim is Ann's best friend. Let R be the following relation on A and B: a Rb if a is related to b. Which of the pairs below are not in this relation?

A. it is impossible to tell
B. (Ann, Jim)
C. (Kim , Ann)
D. (Jim , Ann)
E. (Tom , Jim)
F. (Tom , Ann)
G. all these statements are true

Answer 1

The pairs that are not in the relation R, given that R is defined by a blood relation, would be (Kim, Tom) and (Kim, Jim) since Kim is not a sibling but only a friend of Ann.

Step-by-step explanation:

The question pertains to the concept of relations in a set. We are given two identical sets, A and B, and a relation R defined on A and B such that a R b if a is related to b. The elements Tom, Jim, and Ann are siblings, and Kim is Ann's best friend. Since Kim is only a friend and not a sibling, she is not related by blood to any of the others. Therefore, the pairs that are not in this relation because they are not siblings would be:

(Kim, Tom)(Kim, Jim)

All other given pairs represent sibling relationships and, consequently, are in the relation R.

The question also relates to concepts of mutual exclusivity and dependent events in probability, as evident from the provided examples. However, those examples are not directly relevant to answering the main question.