## Thinking Mathematically (6th Edition)

$n(A\cup B)=27$
$A$ contains $8$ letter and $9$ numbers, for a total of $8+9=17$ elements. $B$ contains $7$ letters and $10$ numbers, for a total of $7+10=17$ elements. $A\cap B$ contains $4$ letters and $3$ numbers for a total of $4+3=7$ elements. The formula for the cardinal number of the union of two sets is the same regardless of whether certain elements are numbers or letters or something else entirely. The formula is: $n(A\cup B)=n(A)+n(B)-n(A\cap B)=17+17-7=27$