Shelly, Jess, and Andrea are all working at an amusement park for the summer. The manager finds out that one of them left the key in the door to the security office. When he asked them who did it, they replied:

Shelly: Andrea did it.
Jess: Shelly did not do it.
Andrea: I didn’t do it.

The manager believed Jess. Use an indirect proof to show that Shelly did not leave the key in the security office door.

Hint: Begin by assuming Shelly did leave the key in the door.

Question

Shelly, Jess, and Andrea are all working at an amusement park for the summer.  The manager finds out that one of them left the key in the door to the security office.  When he asked them who did it, they replied:
 
Shelly: Andrea did it.
Jess: Shelly did not do it.
Andrea:  I didn’t do it.
 
The manager believed Jess. Use an indirect proof to show that Shelly did not leave the key in the security office door.
 
Hint: Begin by assuming Shelly did leave the key in the door.

anonymous · Answer

shelly's statement that andrea did it is FALSE because we're assuming shelly did it. Jess's statement that shelly didn't do it is also FALSE because we're again assuming that shelly did do it. Andrea's statement that she didn't do it is TRUE because it was shelly who supposedly did it. Since two out of three statements are false, we can conclude that the opposite is true, Shelly did leave the key in the door.