Let n be a positive integer and define [n] to be the set of the first n positive integers. that is, [n] = {1, 2, 3, . . , n}. we want to select two disjoint, possibly empty subsets a, b of [n]. in how many ways can we do this?

There are ways of doing this

Hi!

To solve this problem we can think in term of binary numbers. Let's start with an example:

n=5,  A = {1, 2 ,3},  B = {4,5}

We can think of A as 11100, number 1 meaning "this element is in A" and number 0 meaning "this element is not in A"

And we can think of B as 00011.

Thinking like this, the empty set is 00000, and [n] =11111 (this is the case A=empty set, B=[n])

This representation is a 5 digit binary number. There are of these numbers. Each one of this is a possible selection of A and B. But there are repetitions: 11100 is the same selection as 00011. So we have to divide by two. The total number of ways of selecting A and B is the .

This can be easily generalized to n bits.

answer: i would say b

step-by-step explanation:

with the way the question is worded, i believe b is the answer

the cost of the apple depends on the weight

the camry sales+accord sale=828,000. to make it so the two numbers are 18 thousand apart and still equal 828,000, you first need to find out what half of 828,000 is. 828,000/2=414,000. for the two numbers to equal 828,000, you have to add the same amount as you subtract from the middle. in this case, the number is 9,000 because it's half of 18,000. to equal 828,000, you have to add 9,000 to 414,000 for the camry and subtract 9,000 from 414,000 for the accord. 414,000+9,000=423,000.

414,000-9,000=405,000.

423,000+405,000=828,000.

423,000-405,000=18,

hope it