suppose that W is a set which has 255 proper subsets. Determine the cardinality of w
To determine the cardinality of set W, we need to find out how many elements are there in set W.
Given information states that set W has 255 proper subsets. A proper subset is a subset that does not include the entire set itself. To find the cardinality of W, we can use the fact that the number of proper subsets of a set with n elements is given by 2^n - 1.
In this case, we have 255 = 2^n - 1.
To solve for n, we can take the logarithm of both sides of the equation:
log2(255 + 1) = log2(2^n)
log2(256) = n * log2(2)
n = log2(256)
Using a calculator or mathematical software, we find that n ≈ 8.
Therefore, the cardinality of set W is 2^8 = 256.