Discrete Structures : One-to-one, Onto and Range

Let f(x) = x^2 + x - 12. Consider f as a function from the reals to the reals. Is f one-to-one? Is f onto? What is the range of f?

Discrete Structures : Onto and One-to-one

Prove or disprove (find a counterexample) : If A C B and f : A --> B is an onto function (the range of f is all of B), then f is one-to-one and A =B. Please see the attached file for the fully formatted problem.

Discrete Structures : Reflexive, Symmetric or Transitive Relation

Let S ne the set of all strings of a's and b's. Let R be the relation on S defined by... x and y begin with different symbols. Determine, and prove your answers, whether or not R is reflexive, symmetric or transitive. Please see the attached file for the fully formatted problems.

Discrete Structures : Congruences

Construct addition and multiplication tables for arithmetic modulo 11. For example, 7 + 8 mod 11 is 4 and 7*8 mod 11 is 1 so the entry in row 7, column 8 would be 4 for the addition table and 1 for the multiplication table. Use your tables to solve each of the following congruences: a. 3x+2≡8 (mod11) b. 3x-5≡2 (m ...continues

Discrete Structures : Reflexive, Symmetric or Transitive Relations

Let S be the set of all strings of a’s and b’s. Let R be the relation on S defined by....x and y begin with different symbols. Determine and prove your answers, whether or not R is reflexive, symmetric or transitive.

Connected Graph

See attached

Truth tables

Let p represent some false statement and let q represent some true statement. What is the truth value of each of the following: a. ~(~p v q) b. ~(p v q) c. (~p) v q

Handshakes

On the first day of math class, 20 people are present in the room. To become acquainted with one another, each person shakes hands just once with everyone else. How many handshakes take place?

Mid Span Deflection : Transposing Equations and Solving by Substitution

The equation for the mid-span deflection of a simply supported beam carring a uniformly distributed load can be determined from. M=5WL^3 / 384EI AND I=bd^3 / 12 where: M = mid-span deflection W = total load L = span E = Young's modulus of elasticity I = ...continues

Discrete Structures : Sequences, Subsequences and Remainders

1. How do I prove that in a group of n people there are two people with the same number of acquaintances within the group? 2. Prove that given a sequence of twelve integers, a1, a2, …,a12, there is a subsequence aj, aj+1, …, ak where 12 divides ∑kn= aa n. 3. A scrape of paper is found in an old desk that read: 72 t ...continues