An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (1)
Count the number of elements in the set: n = 9 .
Calculate the number of subsets using the formula 2 n : 2 9 = 512 .
Calculate the number of proper subsets using the formula 2 n − 1 : 2 9 − 1 = 511 .
The number of subsets is 512 . The number of proper subsets is 511 .
Explanation
Analyze the set Let's analyze the given set and determine the number of subsets and proper subsets. The set is: { f , g , h , i , j , k , l , m , n } .
Count the elements First, we need to determine the number of elements in the set. By counting, we find that there are 9 elements.
Calculate the number of subsets (a) The number of subsets of a set with n elements is given by the formula 2 n . In our case, n = 9 , so the number of subsets is 2 9 . Calculating this, we get 2 9 = 512 .
Calculate the number of proper subsets (b) The number of proper subsets of a set with n elements is given by the formula 2 n − 1 . This is because a proper subset is any subset except the set itself. In our case, n = 9 , so the number of proper subsets is 2 9 − 1 . Calculating this, we get 512 − 1 = 511 .
State the final answer Therefore, the number of subsets is 512, and the number of proper subsets is 511.
Examples
Consider a pizza topping scenario. If you have 9 different toppings available, the number of possible pizzas you can create with any combination of these toppings is the number of subsets (including a pizza with no toppings). The number of pizzas with at least one topping is the number of proper subsets (excluding the pizza with no toppings). This concept is useful in various combinatorial problems where you need to count the number of possible combinations.
