Determine which, if any, of the three statements are equivalent.

I) If it is sunny and the pool is open, then I will go swimming.
II) If I do not go swimming, then it it is not the case that it is sunny or the pool is open.
III) It is sunny and the pool is open, or I will go swimming.

Question

Determine which, if any, of the three statements are equivalent.

I)  If it is sunny and the pool is open, then I will go swimming.
II)  If I do not go swimming, then it it is not the case that it is sunny or the pool is open.
III)  It is sunny and the pool is open, or I will go swimming.

anonymous · Answer

Statements I and II are equivalent, because statement II says that If said person doesn't go swimming, it means that it is not sunny or the pool is not open, which is in conjunction with the first statement, which says that if it is sunny and the pool is open, said person will go swimming.