The following table gives the choices of two individuals, Chloe and Micah, from themenu M = {A, B, C, D}, and each submenu of M with at least two elements.menu or Chloe'ssubmenuchoiceABCDсABCBCABDACDBCDABACADBCBDCDDDCDBACAсBDсMicah'schoiceBDсABDCDBDAAADBBDD(a) For each of Chloe and Micah, determine whether their choice from M satisfies (1)the contraction condition: (II) the expansion condition.(b) Is either Chloe's choice from M or Micah's choice from M reasonable? Briefly jus-tify your answer.

Answered: The following table gives the choices…

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter9: Sequences, Probability And Counting Theory

Section9.5: Counting Principles

Problem 40SE: A family consisting of 2 parents and 3 children is to pose for a picture with 2 family members in...

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Related questions

Question

The following table gives the choices of two individuals, Chloe and Micah, from the
menu M = {A, B, C, D}, and each submenu of M with at least two elements.
menu or Chloe's
submenu
choice
ABCD
с
ABC
BC
ABD
ACD
BCD
AB
AC
AD
BC
BD
CD
D
D
CD
B
AC
A
с
BD
с
Micah's
choice
BD
с
ABD
CD
BD
A
A
AD
B
BD
D
(a) For each of Chloe and Micah, determine whether their choice from M satisfies (1)
the contraction condition: (II) the expansion condition.
(b) Is either Chloe's choice from M or Micah's choice from M reasonable? Briefly jus-
tify your answer.

Expert Solution

Step 1

We have given two individuals Chloe and Micah and a menu as a set $M = \{A, B, C, D\}$ such that each sub-menu of $M$ has at least two elements from $M$ .

(a)

(i)

Contradiction condition:

if $P$ and $Q$ be two set Non-empty such that $P \subset Q$ , then,

if $x \in P \subset Q$ such that if $x \in C (Q)$ , it means $x \in C (P)$ .

which implies that the contradiction condition satisfies, where $C$ denotes, $C (T) = \{x \in T; \forall y \in T\}$ and $T be any \neq Q set$ .

Here, $M = \{A, B, C, D\}$ and for every choice Chloe and Micah we have that they are subset of their menu or sub-menu corresponding, and if a element belong to menu or sub-menu then it does not belong to individual choice which implies that the contradiction condition fails.

For example:

Chloe first choice is $C$ $M e n u = \{A, B, C, D\}; L \subset M$ but $C \in M \neq C \in L$ .