Discrete Mathematics One Question

in this assignment you have to use logic such truth tables and logically equivalent statements + rule of inference.

Read it carefully !!!!!! I need it in few hours 


After baking a pie for the two nieces and two nephews who are visiting her, Aunt Nellie leaves the pie on her kitchen table to cool. Then she drives to the mall to close her boutique for the day. Upon her return she finds that someone has eaten one-quarter of the pie. Since no one was in her house that day (except for the four visitors) Aunt Nellie questions each niece and nephew about who ate the piece of pie. The four suspects” tell her the following:

a. Charles: Kelly ate the piece of pie.
b. Dawn: I did not eat the piece of pie.
c. Kelly: Tyler ate the pie.
d. Tyler: Kelly lied when she said I ate the pie.

If only one of these four statements is true and only one of the four guilty, who is the culprit? Show your work ; explain your reasoning.

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