Question

calculate the number of subsets and the number of proper subsets for the given set. {x|x∈n and 10<x<15} number of subsets: \boxed{}

Explanation:

Step1: List elements of the set

The set is $\{11, 12, 13, 14\}$, so $n=4$ (number of elements).

Step2: Calculate total subsets

Use formula $2^n$: $2^4 = 16$

Step3: Calculate proper subsets

Use formula $2^n - 1$: $2^4 - 1 = 15$

Answer:

Number of subsets: 16
Number of proper subsets: 15