Question

Write the converse, inverse, and contrapositive of: "If voltage increases, then current decreases".

Hint:

Remember: Contrapositive = Swap + Negate both parts. It is always logically equivalent to the original statement.

Answer 1

Concept: Let the statement be of the form: \[ \text{If } p \text{ then } q \] where:

Converse: If \( q \rightarrow p \)
Inverse: If \( \neg p \rightarrow \neg q \)
Contrapositive: If \( \neg q \rightarrow \neg p \)

Step 1: Identify statements

\( p \): Voltage increases
\( q \): Current decreases

Step 2: Write required forms Converse: If current decreases, then voltage increases. Inverse: If voltage does not increase, then current does not decrease. Contrapositive: If current does not decrease, then voltage does not increase. Explanation: The converse swaps hypothesis and conclusion, the inverse negates both parts, and the contrapositive swaps and negates both. The contrapositive is logically equivalent to the original statement.