absolute value symbol l l
First look at some small finite sets:
Let A={1,5,9}
B={U,V,W,X,Y,Z}
C={Barrak Obama, Joe Biden, Hillary Clinton}
Fill in the blanks with one of the symbols <,>,=
lAl lBl
lAl lCl
lAl lAl
lBl lCl
Describe how you decided the comparative sizes of A,B, and C.
To determine the comparative sizes of sets A, B, and C, we need to understand the concept represented by the absolute value symbol "l l" in this context.
The absolute value symbol "l l" is typically used to denote the cardinality, or the size, of a set. The cardinality of a set refers to the number of elements present in that set.
Let's analyze each of the given sets using the absolute value symbol:
For set A: A={1, 5, 9}
- The absolute value of set A, denoted as lAl, would be 3. This is because set A has three distinct elements (1, 5, and 9).
For set B: B={U, V, W, X, Y, Z}
- The absolute value of set B, denoted as lBl, would be 6. This is because there are six distinct elements in set B (U, V, W, X, Y, and Z).
For set C: C={Barack Obama, Joe Biden, Hillary Clinton}
- The absolute value of set C, denoted as lCl, would be 3. This is because set C consists of three distinct elements (Barack Obama, Joe Biden, and Hillary Clinton).
Now, let's fill in the blanks using the comparison symbols <, >, or =:
lAl lBl (lA is 3, lB is 6)
- Since 3 is less than 6, we can write lAl < lBl.
lAl lCl (lA is 3, lC is 3)
- Since both sets have the same number of elements, we can write lAl = lCl.
lAl lAl (lA is 3, lA is 3)
- Since both sets have the exact same number of elements, we can write lAl = lAl.
lBl lCl (lB is 6, lC is 3)
- Since 6 is greater than 3, we can write lBl > lCl.
In summary, we determined the comparative sizes of sets A, B, and C by calculating the cardinality using the absolute value symbol, and then comparing those values using the appropriate comparison symbols.