Relations and equivalence relations Consider the people in a

Relations and equivalence relations Consider the people in a class on the first day of the semester. Each student in the class may or may not know the first name of another student in the class. Mathematically we can describe this social phenomenon using a relation. Specifically, if we want to describe the fact that Cedric knows Alfred\'s first name, then we can use an ordered pair. We can write the ordered pair (Cedric, Alfred) to indicate that Cedric knows Alfred\'s first name. (Why do we require the order?) Hence, the relation knows the first name of is the set of ordered pairs (x, y) where person x knows person y\'s first name. Let S and T be sets. A relation Rscr on S and T is a subset of S times T. That is Rscr Subset S times T. If Rscr is a relation, then we can write (s, t) Element Rscr or s Rscr t to indicate that (s, t) is an element of the relation. If (s, t) is an element of a relation, then we say that \"s is related to t.\" Sometimes we will use mathematical shorthand and write s Tilde t. Create a relation Kscr that describes the situation in Example 5.1. Use a hypothetical class of at least six people where no one knows everyone\'s first name on the first day of class. Define a relation Wscr on Nopf times Nopf by (m, n) Element Rscr if 2m

Solution

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for this type of hypothetical example

R =[(cedric,alfred), (soma, sona),(anmon, james),(truil, reash), (bagata, ninim)] can be a perfect relation example

where each one knows the first name

for the second part we again can use

R =[(cedric,alfred), (soma, sona),(anmon, james),(truil, reash), (bagata, ninim)] assuming here that no one knows others nAMe