Calculate the cardinal of $$A \cup B$$ and $$A \times B$$ if $$A=\{1,3,4,5,6,7\}$$ and $$B=\{3,4,7,8,9\}$$.
See development and solution
Development:
First the cardinal ones are calculated of $$A$$ and $$B$$: $$$card(A)=6$$$ $$$card(B)=5$$$ Next the intersection of both sets is calculated: $$$A\cap B=\lbrace3,4,7\rbrace$$$ and later its cardinal one: $$$card(A\cap B)=3$$$ Finally, to calculate $$$card(A\cup B)$$$ we apply the principle of addition, and to calculate the cardinal one of $$A\times B$$ we apply the principle of multiplication $$$card(A\cup B)=card(A)+card(B)-card(A\cap B)=6+5-3=8$$$ $$$card(A)\times card(B)=6\cdot5=30$$$
Solution:
$$card(A\cup B)=8$$; $$card(A)\times card(B)=30$$