Calculus 3 sets

Question

Find the following cardinalities:

a. A={5,10,15,...,75}

  

b. A= { x ∈ Z : −100 ≤ x ≤ −17 }

  

c. A= { x ∈ N : x ≤ 10 } , B = { x ∈ N : x ≤ 12 }

  

Answer 1

The cardinality of a finite set is the number of elements in it.

a. {5, 10, .. 75} has 15 elements (things).

b. A= { x ∈ Z : −100 ≤ x ≤ −17 } has 84 elements. Z is the set of integers. x ∈ Z means x is in the set of integers.

c. A= { x ∈ N : x ≤ 10 } has 10 elements. N is the set of natural numbers (positive numbers).

B = { x ∈ N : x ≤ 12 } has 12 elements.

Double check my counting.