Let r be the relation consisting of all pairs (x, y) such that x and y are strings of uppercase and lowercase english letters with the property that for every positive integer n, the nth characters in x and y are the same letter, either uppercase or lowercase. show that r is an equivalence relation.

An equivalence relation R is a binary relation that is reflexive, symmetric and transitive.

Step-by-step explanation:

An equivalence relation R is a binary relation that is reflexive, symmetric and transitive.

Reflexive:

R is said to b reflexive if a R a

Symmetric:

R is said to be symmetric if a R b implies b R a

Transitive:

R is said to be transitive if a R b, b R c implies a R c

Given: Let R be the relation consisting of all pairs (x,y) such that x and y are strings of uppercase and lowercase English letters with the property that for every positive integer n, the nth characters in x and y are the same letter, either uppercase or lowercase.

To prove:

R is an equivalence relation.

Reflexive:

As the nth characters in x and x are the same letter, R is reflexive

Symmetric:

If  nth characters in x and y are the same letter then clearly nth characters in y and x are the same letter

Transitive:

If  nth characters in x and y are the same letter and nth characters in y and z are the same letter then nth characters in x and z are the same letter.

So, R is an equivalence relation.

answer: a

step-by-step explanation:

if xy ~ yz therefore xy would be the same length as yz

step-by-step explanation:

ok one would be money, and the other would be refreshments or something similar. if each bag of popcorn is 5.00 and each drink is half of that that means drinks are 2.50 the proper way to do that would to look and see how much of each you can buy without exceeding a limit of 30.00