"If a plant is a fern, it does not produce flowers." This plant produces flowers. Is it a fern?MaybeNoYes

Break Down the Problem

1. Identify the statement: "If a plant is a fern, it does not produce flowers."
2. Analyze the implication of the second part: "This plant produces flowers."

Relevant Concepts

• The initial statement is a conditional statement (if-then) in logic.

• The logic can be expressed as:

  • If $P$ (the plant is a fern), then $Q$ (the plant does not produce flowers).

• The contrapositive of this statement is:

  • If $Q$ is false (the plant produces flowers), then $P$ is also false (the plant is not a fern).

Analysis and Detail

1. The initial statement indicates that being a fern implies the absence of flowers.
2. Since the plant in question produces flowers, we can state that $Q$ is false.
3. Using the contrapositive, we can conclude that the plant cannot be a fern.

Verify and Summarize

• The original statement establishes a clear relationship: if it is a fern, it cannot produce flowers.
• Since this plant produces flowers, it negates the possibility of it being a fern.

Final Answer

No, it is not a fern.