Set builder notation translation and cardinality

Question

Given the following:S = {(A, B) | A ⊆ {1, 2, . . . , n}, B ⊆ {1, 2, . . . , n}, |A ∩ B| ≥ 1}, how can I translate this in terms of english and how would one go about finding the cardinality of the set? 

Answer 1

Hi Carlos,

 

I will take a stab at this since no one else has.

 

S = {(A, B) |   states "S is the collection of elements in the sets A and B such that"

 

A ⊆ {1, 2, . . . , n} states "A is a subset of the numbers 1,2,..up to the number n"

 

It means in English that A has some and might have all of the integers starting at 1 and ending at n

 

B ⊆ {1, 2, . . . , n}  states "B is a subset of the numbers 1,2,..up to the number n" 

 

 

In English, it means B has some and might have all of the integers starting at 1 and ending at n

 

|A ∩ B| ≥ 1   states 'the cardinality of the intersection of the sets A and B is greater than or equal to 1"

 

in English, at least 1 number is in both set A and set B

 

Cardinality refers to the number of elements in a set

 

I can't give you a number value for the cardinality of the set except that it is 1 or larger.

 

I'm hoping some other tutors might weigh in on this

 

 

 

 

 

 

 

Please send me as mesage and tell me if it helped