11 - 20.Consider a system where children in a classroom choose different flavors of ice cream.Suppose we have the following axioms:(A1) There are exactly five flavors of ice cream: vanilla, chocolate, strawberry,cookie dough, and bubble gum.(A2) Given any two distinct flavors, there is exactly one child who likes these.(A3) Every child likes exactly two flavors of ice cream.a. Construct a model for the axiomatic system. How many children are in theclassroom?b. Prove that any pair of children likes at most one common flavor usingmathematical language.c. Is Axiom 3 independent? Justify.

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Answered: Consider a system where children in a…

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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A math instructor has 46 calculators in her office. Of them, 22 have dead batteries, 28 have cracked displays, and 24 have missing buttons. Of those with dead batteries, 16 have cracked displays and 11 have missing buttons. Of those with cracked displays, 18 have missing buttons. There are 9 with dead batteries, cracked displays, and missing buttons. How many calculators does she have with nothing wrong with them? (A) 6 (В) 4 (C) 5 (D) 9 (E) 8 (F) 3 (G) 1 (H)
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Discrete Math. I just need help understanding the set up. Part A is 100 ways and Part B is 30,240

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