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Found in: Page 23

Discrete Mathematics and its Applications

Book edition 7th
Author(s) Kenneth H. Rosen
Pages 808 pages
ISBN 9780073383095

When planning a party you want to know whom to invite. Among the people you would like to invite are three touchy friends.You know that if Jasmine attends, she will become unhappy if Samir is there, Samir will attend only if Kanti will be there, and Kanti will not attend unless Jasmine also does.Which combinations of these three friends can you invite so as not to make someone unhappy? Exercises relate to inhabitants of the island of knights and knaves created by Smullyan, where knights always tell the truth and knaves always lie. You encounter two people, and . Determine, if possible, what and are if they address you in the ways described. If you cannot determine what these two people are, can you draw any conclusions?

There are just two options: Jasmine and Kanti together or Jasmine by alone.

See the step by step solution

Introduction

In response to such directions, truth-tellers frequently supply more comprehensive information in order to show their innocence. Liars, on the other hand, want to keep their mistakes hidden.

Explanation

From the given data,

To provide advice on which combinations and three Mends you should invite so that no one is disappointed.

It is necessary to create a mix in which no one is dissatisfied.

The statement is,

Jasmine attends the party$˸\mathrm{j}$

Samir attends the party$˸\mathrm{s}$

Kanti attends the party$˸\mathrm{k}$

Truth table

 Expressing in the form of truth table
j$\mathrm{s}$$\mathrm{k}$$¬\mathrm{s}$$¬\mathrm{k}$$\mathrm{j}\to ¬\mathrm{s}$$\mathrm{k}\to ¬\mathrm{s}$$¬\mathrm{k}\vee \mathrm{j}$
TTFFTFTT
TTTFFFTT
TFFTTTTT
TFTTFTFT
FTFFTTTF
FTTFFTTF
FFFTTTTT
FFTTFTFF

From the truth table,

If Jasmine is willing to come. If Samir is present, she will be displeased ${\mathbf{:}}{\mathbf{j}}{\mathbf{\to }}{\mathbf{¬}}{\mathbf{s}}$

If Samir is present, he will only participate if Kanti is also there${\mathbf{:}}{\mathbf{k}}{\mathbf{\to }}{\mathbf{s}}$

Kanti won't show up till Jasmine arrives${\mathbf{:}}{\mathbf{k}}{\mathbf{\to }}{\mathbf{j}}{\mathbf{⇔}}\left(¬k\vee j\right)$

Thus, there are just two options: Jasmine and Kanti together or Jasmine by alone.