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 = second moment of area 1. Transpose this equation to make L the subject. 2. Taking care with units, use this transposed equation to find the maximum length of beam that can be used if the midspan deflection is to be limited to 7 mm. W= 12kN E= 10,000 N/mm2 b= 75mm d= 200mm

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 turkeys $X67.9Y The first and last digits of the price were smudged. What are the two smudged digits? 4. Show that from any five integers, not necessarily distinct, one can always choose three of these integers whose sum is divisible by 3.