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**1. Homework Statement**

Four friends have been identified as suspects for a pumpkin smashing. They have made statements to the investigating authorities. (

**i**)Alice said "Carlos did it." (

**ii**)John said "I did not do it." (

**iii**)Carlos said "Diana did it." (

**iv**)Diana said "Carlos lied when he said that I did it."

a) If the authorities also know that exactly one of the four suspects is telling the truth, who did it? Explain your reasoning.

b) If the authorities also know that exactly one is lying, who did it? Explain your reasoning.

**2. Homework Equations**

p = "John did it"

q = "Carlos did it"

r = "Diana did it"

(i) [tex]q[/tex]

(ii) [tex]\neg\,p[/tex]

(iii) [tex]r[/tex]

(iv) [tex]\neg\,r[/tex] or "Carlos lied"

**3. The Attempt at a Solution**

I set up a truth table and reasoned that for a) John did it and for b) Carlos did it. Does that seem right? Is there another way that I should be going about this problem?