Question: If A = {1, 2, 3} and B = {1, 2, 3, 4}, what is the cardinality of A × B?
Options:
3
6
9
12
Correct Answer: 6
Solution:
The cardinality of the Cartesian product A × B is given by |A| * |B|. Here, |A| = 3 and |B| = 4, so |A × B| = 3 * 4 = 12.
If A = {1, 2, 3} and B = {1, 2, 3, 4}, what is the cardinality of A × B?
Practice Questions
Q1
If A = {1, 2, 3} and B = {1, 2, 3, 4}, what is the cardinality of A × B?
3
6
9
12
Questions & Step-by-Step Solutions
If A = {1, 2, 3} and B = {1, 2, 3, 4}, what is the cardinality of A × B?
Correct Answer: 12
Step 1: Identify the sets A and B. A = {1, 2, 3} and B = {1, 2, 3, 4}.
Step 2: Determine the number of elements in set A. There are 3 elements in A.
Step 3: Determine the number of elements in set B. There are 4 elements in B.
Step 4: Use the formula for the cardinality of the Cartesian product, which is |A × B| = |A| * |B|.
Step 5: Substitute the values into the formula. |A × B| = 3 * 4.
Step 6: Calculate the result. 3 * 4 = 12.
Step 7: Conclude that the cardinality of A × B is 12.
Cardinality – The concept of cardinality refers to the number of elements in a set.
Cartesian Product – The Cartesian product of two sets A and B, denoted A × B, is the set of all ordered pairs (a, b) where a is in A and b is in B.
Multiplication of Cardinalities – The cardinality of the Cartesian product A × B is calculated by multiplying the cardinalities of the individual sets: |A × B| = |A| * |B|.
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