Question

set notation
a = {1,2,7,8,10}
b = {1,2,3,4}
c = {2,4,6,8}
(a) list the elements of a ∩ b
(b) list the elements of b ∪ c
(c) find n(b)
(d) find n(a ∪ c)
(e) 3 ∈ b. true or false?
(f) 2 ∈ b ∩ c. true or false?
a = {n,u,m,b,e,r}
b = {e,q,u,a,l}
c = {s,i,x}
(a) list the elements of a ∪ c
(b) list the elements of b ∩ a

Explanation:

Part 1 (Red Box, Numerical Sets)

(a) List the elements of \( A \cap B \)

Step1: Recall intersection definition

Intersection \( A \cap B \) is elements common to both \( A \) and \( B \).
\( A = \{1,2,7,8,10\} \), \( B = \{1,2,3,4\} \)
Common elements: 1, 2.

Step1: Recall union definition

Union \( B \cup C \) is all elements in \( B \) or \( C \) (no duplicates).
\( B = \{1,2,3,4\} \), \( C = \{2,4,6,8\} \)
Combine elements: 1,2,3,4,6,8.

Step1: Recall set cardinality

\( n(B) \) is the number of elements in \( B \).
\( B = \{1,2,3,4\} \), count elements: 4.

Answer:

\( \{1, 2\} \)

(b) List the elements of \( B \cup C \)