Final answer:
The statement "It is false that either our planet is special or it isn't" can be represented as ∼(O∨∼O). Option b is correct.
Step-by-step explanation:
Let's break down the given statement:
"It is false that either our planet is special or it isn't."
Let:
- O be the statement "Our planet is special."
- ~O be the statement "Our planet is not special."
The given statement can be represented as the logical disjunction (OR) of O and ~O, and then negated because it is false:
~(OV ~O)
Now, let's analyze the given options:
A. ~ O V ~~ O
- This simplifies to ~O V O, which is always true (tautology).
B. ∼(O∨∼O)
- This matches the representation of the given statement and is the correct logical form.
C. ∼(O∨∼∼O)
- This simplifies to ∼(O∨O), which is always false (contradiction).
Therefore, the correct option is B: ∼(O∨∼O).