Cardinality of some sets

Statement

Find the cardinality of each set.

(i) $\{a,b,c,d,e,f,g\}$ (ii) $\{2,4,6,4,2\}$ (iii) $\{1,2,\dots,60\}$ (iv) $\{10,11,\dots,99\}$

Solution

(i) Seven distinct elements: $\boxed{7}$. (ii) The distinct elements are $2,4,6$: $\boxed{3}$ (repetitions do not count). (iii) The integers from $1$ to $60$ number $\boxed{60}$. (iv) From $10$ to $99$: $99-10+1 = \boxed{90}$.