Suppose the universal set is U = {1,2, 3, 4, 5, 6, 7, 8, 9, 10}. The bit string representation of the following set where the ith bit in the string is 1 if ith element is in the set and 0 otherwise. {3,5, 6, 9} 0010011010 O 0010110010 O 0110110010 O 0011010010

Show that given any set of 5 natural numbers, there are 3 numbers whose sum is divisible by 3.

A ternary string is an ordered string of characters which consists of digits (0,1, or 2). For example, the ternary string 2122010 consists of exactly 2 zero's, 2 one's and 3 two's; another ternary string meeting these conditions is 0021221. How many ternary strings are there with exactly 3 zero's, 3 one's and 5 two's?

Mathematical logic Suppose that C is generated from a set B={a,b} by the binary operation f and the unitary operation g. List all the elements of C_2. How many elements can C_3 and C_4 have? Remember that C_n is the set of all points x such that some construction sequence of length n ends with x, and then B=C_1⊆C_2⊆C_3⊆⋯. Please be as clear and legible as possible. Show and explain all the steps and use definitions if necessary. Thank you a lot.

Discrete Math:How many bit strings of length 5 contain at least two 1s?

How many permutations are there of the digits in the string 12345 that leave 3 fixed but leave no other integer fixed?

How many elements does the successor of a set with n elements have?

identify all natural numbers having exactly 28 divisors.

Consider a finite universal set of a general nature (please do not specify). What subset of this universal set does the bit string with all zeros represent?

How many three digit passcode can be made from the digits 0-9in the first number is not allowed to be zero?