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

Make a truth table for $p$ it is sunny, $q$ the pool is open, and $r$ I will go swimming as it applies to your three statements and see which (if any) coincide in their truth values.$$\begin{array}{c|c|c|c|c|c}p & q & r & \text{(I)} & \text{(II)} & \text{(III)}\ \hline
T & T & T &? & ? &?\
T & T & F &? & ? &? \
T & F & T &? & ? &? \
T & F & F &? & ? &? \
F & T & T &? & ? &? \
F & T & F &? & ? &? \
F & F & T &? & ? &? \
F & F & F &? & ? &? \
\end{array}$$