Discrete Mathematics Answers

An electrician charges a base fee of $70 plus $50 for each hour of work. Create a table that shows the amount the electrician charges for 1,2,3, and 4 hours of work. Let x represent the number of hours and y represent the amount charged for x hours. Is this relation a function?

Of the members of three athletic teams in a school 21 are in the cricket team, 26 are in the hockey team and 29 are in the football team. Among them, 14 play hockey and cricket, 15 play hockey and football, and 12 play football and cricket. Eight play all the three games. The total number of members in the three athletic teams is

A Function f : Z→Z, f(x) = x+5, is invertible since it has the inverse

function g : Z→Z, g(x) = x−5.

show that

1²+3²⁺5²+.....(2n+1)²=(n+1)(2n+1)(2n+3)/3

where n is a nonnegative integer.

Let R1 and R2 be symmetric relations. Is R1 ∩ R2 also symmetric? Is R1 ∪ R2 also

symmetric?

Determine whether each of these functions is a bijection from R to R (real).a) f (x) = 2x + 1b) f (x) = x2 + 1c) f (x) = x3

Draw the Hasse diagrams of all partial ordered sets with at most 4 elements. Which of these are lattices?

Given the following 2 premises, 1. 𝑝→(𝑞∨𝑟)

2. 𝑞→𝑠

Prove 𝑝→(𝑟∨𝑠) is valid using the Proof by Contradiction method.

An algorithm is a _________ set of precise instructions for performing computation.

show that factorial function is promitive recursive