Suppose A = {1,3,7,11} and B = {3,7,12} . Calculate the following showing the step-by-step process of your calculations
a) |A ∪ B|
b) |A| + |B| - |A ∩ B|
c) A X B
Not sure if I'm doing these right.. would a) be:
{1,3,7,11,12} ? and what steps would I show? what is there to show?
a) $|A \cup B| = |\{1,3,7,11,12\}| = 5$
b) $|A| + |B| - |A \cap B| = |\{1,3,7,11\}| + |\{3,7,12\}| - |\{3,7\}| = 4 + 3 - 2 = 5$
c) $A \times B = \{(a,b) \; | \; a \in A \text{ and } b \in B\} = \{(1,3),(1,7),(1,12),(3,3),(3,7),(3,12),(7,3),(7,7),(7,12),(11,3),(11,7),(11,12)\}$
Also, we see that $|A \times B| = 12$, and in general $|A \times B| = |A| \cdot |B|$.