Problem
Suppose that the universal set S
is defined as S={1,2,⋯,10}
and A={1,2,3}
, B={X∈S:2≤X≤7}
, and C={7,8,9,10}
.
Find A∪B
.
Find (A∪C)−B
.
Find A¯∪(B−C)
.
Do A,B,
and C
form a partition of S
?
Problem
When working with real numbers, our universal set is R
. Find each of the following sets.
[6,8]∪[2,7)
[6,8]∩[2,7)
[0,1]c
[6,8]−(2,7)
Problem
For each of the following Venn diagrams, write the set denoted by the shaded area.
3a
3b
3c
3d
Problem
A coin is tossed twice. Let S
be the set of all possible pairs that can be observed, i.e., S={H,T}×{H,T}={(H,H),(H,T),(T,H),(T,T)}.
Write the following sets by listing their elements.
A
: The first coin toss results in head.
B
: At least one tail is observed.
C
: The two coin tosses result in different outcomes.
Problem
Let A={1,2,⋯,100}
. For any i∈N
, Define Ai
as the set of numbers in A
that are divisible by i
. For example:
A2={2,4,6,⋯,100},
A3={3,6,9,⋯,99}.
Find |A2|
,|A3|
,|A4|
,|A5|
.
Find |A2∪A3∪A5|
.