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

Given Statement (Conditional Statement):
If voltage increases, then current decreases.

Let:
p: Voltage increases
q: Current decreases

So the given statement is:
If p, then q (p → q)

1. Converse:
The converse of a conditional statement is formed by interchanging the hypothesis and the conclusion.

Converse: If current decreases, then voltage increases.
(q → p)

2. Inverse:
The inverse is formed by negating both the hypothesis and the conclusion.

Inverse: If voltage does not increase, then current does not decrease.
(¬p → ¬q)

3. Contrapositive:
The contrapositive is formed by interchanging and negating both the hypothesis and the conclusion.

Contrapositive: If current does not decrease, then voltage does not increase.
(¬q → ¬p)

Conclusion:
– 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.