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logicfirst-order-logic

Symbolic logic equivalency


Is there any difference between these two statements, given the following language??

  1. Ben likes dogs and either John or Mary likes dogs.
  2. Ben likes dogs and John or Mary likes dogs.

Using:

B: Ben likes dogs.
J: John likes dogs.
M: Mary likes dogs.

I have B & (J V M) for both...

I'm limited to & () V ~ as my symbols


Solution

    1. B & ((J & ~M) V (~J & M))
    2. B & (J V M)