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?

maths problem

The equation for the mid-span deflection of a simply supported beam carring a uniformly distributed load can be determined from. M=5WL3 devieded by 384EI AND I=bd3 devieded by 12 (the 3 after the L is cubed also after the bd, dont know how to put sign for cubed) where: M = mid span deflection W = total load L = span E = young's modulus of elasticity I = second moment of area question 1; transpose this equation to make L the subject. question 2; taking care with units, use this transposed equation to find the maximum length of beam that can be used if the mid span deflection is to be limitedto 7mm. W= 1... click for more

Problem Solving

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? (Am thinking this is a pigeon hole problem) 2. Prove that given a sequence of twelve integers, a¬1, a¬2, …,a12, there is a subsequence aj, aj+1, …, ak where 12 divides ∑kn= aa n. Please see attached.