Let and List all the elements of the following sets.
A = {1,2} and B = {0,1,2}
A x A
A x B
B x A
A x B x A
how do i do this?
A=m,a,t,e,
Thomas
To find the elements of the Cartesian product of two sets A and B, you need to pair each element of set A with every element of set B. The resulting pairs will form the elements of the Cartesian product set. Here's how you can find the elements for each of the given cases:
1. A x A:
In this case, you need to pair each element of set A with every element of set A.
A = {1, 2}
A x A = {(1, 1), (1, 2), (2, 1), (2, 2)}
2. A x B:
In this case, you need to pair each element of set A with every element of set B.
A = {1, 2}
B = {0, 1, 2}
A x B = {(1, 0), (1, 1), (1, 2), (2, 0), (2, 1), (2, 2)}
3. B x A:
In this case, you need to pair each element of set B with every element of set A.
B = {0, 1, 2}
A = {1, 2}
B x A = {(0, 1), (0, 2), (1, 1), (1, 2), (2, 1), (2, 2)}
4. A x B x A:
In this case, you need to pair each element of the first set (A) with every element of the second set (B), and then pair the resulting pairs with every element of set A again.
A = {1, 2}
B = {0, 1, 2}
A x B = {(1, 0), (1, 1), (1, 2), (2, 0), (2, 1), (2, 2)}
Then, pair the resulting tuples with every element of set A.
A x B x A = {((1, 0), 1), ((1, 0), 2), ((1, 1), 1), ((1, 1), 2), ((1, 2), 1), ((1, 2), 2), ((2, 0), 1), ((2, 0), 2), ((2, 1), 1), ((2, 1), 2), ((2, 2), 1), ((2, 2), 2)}
You can use the same approach to find the elements of the Cartesian product of any two sets. Just pair every element of the first set with every element of the second set.