Question

Determine which, if any, of the three statements are equivalent.
I) If it is not raining, then I will go jogging.
II) Either it is raining or I will go jogging.
III) If it is raining, I will not go jogging.

Answer 1

u can write those propositions like this
I) \(\neg p\to q\)
II) \(p\vee q\)
III) \(p\to\neg q\)

Answer 2

1 and 3 i think

Answer 3

\[ \large \neg p\to q\equiv\neg(\neg p)\vee q\equiv p\vee q \]

Answer 4

1 and 3 I am pretty sure...