look at the following conditionals: if vincent is playing the piccolo, then dana is not playing the…

look at the following conditionals: if vincent is playing the piccolo, then dana is not playing the mandolin. if vincent is not playing the piccolo, then dana is playing the mandolin. is the second conditional the contrapositive, converse, or inverse of the first conditional? contrapositive converse inverse

look at the following conditionals: if vincent is playing the piccolo, then dana is not playing the mandolin. if vincent is not playing the piccolo, then dana is playing the mandolin. is the second conditional the contrapositive, converse, or inverse of the first conditional? contrapositive converse inverse

Answer

Brief Explanations:

Let (p) be "Vincent is playing the piccolo" and (q) be "Dana is not playing the mandolin". The first conditional is (p\rightarrow q). The second conditional: if Vincent is not playing the piccolo ((\neg p)), then Dana is playing the mandolin ((\neg q)), which is (\neg p\rightarrow\neg q). The inverse of (p\rightarrow q) is formed by negating both the hypothesis and the conclusion, which is exactly (\neg p\rightarrow\neg q).

Answer:

inverse