infinites
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 of cardinality, which refers to the number of elements in a set.
For set A={1,5,9}, we can see that there are three elements in the set: 1, 5, and 9. Therefore, the cardinality of set A is 3.
For set B={U,V,W,X,Y,Z}, we have six elements: U, V, W, X, Y, and Z. Hence, the cardinality of set B is 6.
Lastly, for set C={Barack Obama, Joe Biden, Hillary Clinton}, we have three elements again: Barack Obama, Joe Biden, and Hillary Clinton. Thus, the cardinality of set C is 3.
Now, let's compare the sizes of these sets using the absolute value symbol | |. In this case, if two sets have the same cardinality, we use the equality symbol (=) between them. If one set has a greater cardinality than the other, we use the greater than symbol (>). And if a set has a smaller cardinality, we use the less than symbol (<).
Using this understanding, we can now fill in the blanks:
|A| > |B| (Since the cardinality of A is 3, which is greater than the cardinality of B, which is 6)
|A| < |C| (The cardinality of A is 3, less than the cardinality of C, also 3, thus they are not equal)
|A| = |A| (Both sides have the same cardinality, which is 3)
|B| < |C| (The cardinality of B is 6, greater than the cardinality of C, which is 3)
Therefore, we have successfully compared the sizes of sets A, B, and C using their cardinalities and filled in the blanks with the appropriate symbols.