If the weather is not cold, Bud will go swimming.
The weather is cold, or Bud will not go swimming.

determine whether the two statements are logically equivalent. Justify your answer.

Question

If the weather is not cold, Bud will go swimming.
The weather is cold, or Bud will not go swimming.
 
determine whether the two statements are logically equivalent. Justify your answer.

anonymous · Answer

To proof equivalence you need to prove two things: that the first statement follows from the second and that the second statement follows from the first.

anonymous · Answer

ok?

anonymous · Answer

I have the feeling they are not equivalent, so let's try to prove that. Let's assume the first statement is true. If it follows that the second statement is false, then surely they can't be equivalent.

So let's assume "If the weather is not cold, Bud will go swimming"
If the weather is not cold, the weather is not cold and bud will go swimming. So none of the two things are true from the second statement in that case. So the second statement is false. So they are not equivalent.

turingtest · Answer

$$\neg p\implies q$$$$p\vee\neg q$$I think the "or" throws a monkey wrench in it... so I agree with Tomas9

anonymous · Answer

Same