(Solved): Discrete math Let the set of Binary numbers is B={0,1}. a. Determine its Cartesian Product (for exam ...

Expert Answer

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a. Here are the step-by-step instructions to find the Cartesian product of the set B = {0, 1} with itself:
Write down the set  
To find the Cartesian product B × B, take each element of B and pair it with every element of B. To do this, write down all possible ordered pairs of elements from B. The first element in each pair is an element of B, and the second element in each pair is also an element of B. Since B has two elements, there are two choices for each position in the ordered pair. Therefore, there are 2 x 2 = 4 possible ordered pairs. To make sure we don't miss any pairs, we can systematically list all possible combinations of the elements of B:
(0, 0)
(0, 1)
(1, 0)
(1, 1)
These are the four elements of the Cartesian product B × B.
Write down the Cartesian product: B × B = {(0, 0), (0, 1), (1, 0), (1, 1)} Each element of the Cartesian product is an ordered pair, where the first element comes from the first copy of B, and the second element comes from the second copy of B. For example, the ordered pair (0, 1) means "take 0 from the first copy of B and 1 from the second copy of B".
That's it! The Cartesian product of the set B = {0, 1} with itself is B × B = {(0, 0), (0, 1), (1, 0), (1, 1)}.



In this case, we are finding the Cartesian product of the set B with itself, which means we are pairing each element of B with every other element of B. Since the set B has only two elements, which are 0 and 1, there are only two possible choices for each position in the ordered pair - the first element can be either 0 or 1, and the second element can also be either 0 or 1.
So, for the first position in the ordered pair, we have 2 choices (either 0 or 1), and for the second position, we also have 2 choices. Therefore, the total number of possible ordered pairs is the product of the number of choices for each position, which is 2 x 2 = 4.