Calculate number of elements in a set How many natural numbers are there below 1000 that are multiples of 3 or that contain 3 in any digit of the number?
My effort : Here we need to calculate union of two set. First set is natural number which are multiple of 3. So it's cardinality will be the nearest integer of 1000/3, which will be 333. But I am confused with second set.
Any help/hint in this regards would be highly appreciated. Thanks in advance!

How many numbers have $3$ as a first digit?  How many number that do not have $3$ as a first digit have $3$ as a second?  How many that do not have $3$ in one of the first two positions have $3$ in the third?  Add these together to answer your question.  You can't just add this to $333$ because all the ones that are multiples of $3$ and have a $3$ in them have been counted twice.
