Question

the venn diagram here shows the cardinality of each set. use this to find the cardinality of the given set.
n (a∪b) = \boxed{}

Explanation:

Step1: Identify all regions in $A\cup B$

The regions are: only $A$ (12), $A$ and $B$ only (4), $A$ and $C$ only (7), all three sets (2), only $B$ (8), $B$ and $C$ only (5).

Step2: Sum all the cardinalities

$12 + 4 + 7 + 2 + 8 + 5$

Step3: Calculate the total

$12+4=16$; $16+7=23$; $23+2=25$; $25+8=33$; $33+5=38$

Answer:

38