D421 Discrete Math: Functions and Relations - Set 3 - Part 3

Correct Answer: A sequence of n binary digits (0s and 1s)

A bit string of length n is an ordered sequence of n bits, each 0 or 1, and there are 2^n such strings.

Correct Answer: 16

Each of the 4 positions has 2 choices, giving 2^4 = 16 possible bit strings.

Correct Answer: A division into non-empty disjoint subsets whose union is the whole set

A partition splits a set into non-overlapping, non-empty subsets (blocks) that together cover the entire set.

Correct Answer: An equivalence relation induces a partition into equivalence classes

Every equivalence relation on a set produces a partition into equivalence classes, and every partition defines an equivalence relation.

Correct Answer: Clock arithmetic

Modular arithmetic is called clock arithmetic because values wrap around after reaching the modulus, like hours on a clock.

Correct Answer: The number of k-element subsets of an n-element set

C(n, k) counts the k-element subsets of an n-element set and appears as a coefficient in the binomial theorem.

Correct Answer: The sum of the two entries above it

Each interior entry of Pascal's triangle is the sum of the two entries diagonally above it, reflecting the identity C(n,k) = C(n−1,k−1) + C(n−1,k).

Correct Answer: A power of a binomial such as (x + y)^n

The binomial theorem expands (x + y)^n as a sum of terms C(n, k) x^(n−k) y^k for k from 0 to n.

Correct Answer: A finite sequence of well-defined steps to solve a problem

An algorithm is a finite, ordered set of unambiguous instructions that transforms input into a desired output.

Correct Answer: It provides the theory behind logic, algorithms, and data structures

Discrete mathematics underpins computer science through logic, set theory, combinatorics, graph theory, and algorithm analysis, which model computation.