Find the cardinal number for the following sets A = {106, 107, 108, 109,...,142} B= {106, 108, 110, . . ., 256} n(A) =

Question

Help with this math question i can't seem to find the missing number 

Answer 1

A={106, 107, 108, 109, ..., 142}

you have consecutive integers

if you had 1, 2, 3, ..., 142, you would have 142 numbers but you are missing 1, 2, 3, ..., 105

142-105=37 numbers

or, 142-106=36, 36+1=37

 

B={106, 108, 110, ..., 256}

you have multiples of 2

if you had 2, 4, 6, 8, ..., 256, you would have 256/2=128 numbers

you are missing 2, 4, 6,..., 104, which totals 52 numbers

128-52=76 numbers

or, 256-106=150, 150/2=75, 75+1=76