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?
The second conditional is the contrapositive of the first conditional.
The second conditional is the contrapositive of the first conditional.
To determine the relationship between different conditionals, we need to understand their various forms. Let's break down the two conditionals given:
1) "If Vincent is playing the piccolo, then Dana is not playing the mandolin."
This is a conditional statement in the form "If P, then Q". The antecedent "P" is "Vincent is playing the piccolo," and the consequent "Q" is "Dana is not playing the mandolin."
2) "If Vincent is not playing the piccolo, then Dana is playing the mandolin."
This is also a conditional statement of the same form, "If P, then Q". Here, the antecedent "P" is "Vincent is not playing the piccolo," and the consequent "Q" is "Dana is playing the mandolin."
Now let's determine the relationship between the first and second conditional:
- The contrapositive of a conditional statement switches both the antecedent and consequent, forming a new statement. In this case, the contrapositive of the first conditional would be: "If Dana is playing the mandolin, then Vincent is not playing the piccolo."
- The converse of a conditional statement only switches the antecedent and consequent. So, for the first conditional, the converse would be: "If Dana is not playing the mandolin, then Vincent is playing the piccolo."
- The inverse of a conditional statement negates both the antecedent and the consequent. The inverse of the first conditional is: "If Vincent is not playing the piccolo, then Dana is playing the mandolin."
Comparing the second conditional to the three options:
- The contrapositive of the first conditional does not match the second conditional.
- The converse of the first conditional does not match the second conditional.
- The inverse of the first conditional does match the second conditional.
Therefore, the second conditional matches the inverse of the first conditional.