Final answer:
We cannot conclude that rectangle LMNO has side lengths of 3 cm and 4 cm solely based on its area being 12 cm², as the side lengths are not confirmed by the second statement, thus not properly applying the Law of Detachment.
Step-by-step explanation:
The question involves the use of the Law of Detachment in deductive reasoning within mathematics. The Law of Detachment, also known as modus ponens, is a logical form that states if the following two statements are true: 'If p, then q' and 'p is true', then we can conclude 'q is true'. In the given scenario, the first statement is 'If a rectangle has side lengths 3 cm and 4 cm, then it has an area of 12 cm2'. The second statement is 'Rectangle LMNO has area 12 cm2'.
To use the Law of Detachment, we need the second statement to confirm that rectangle LMNO has side lengths of 3 cm and 4 cm. However, we are only told the area of rectangle LMNO, not its side lengths. Therefore, based on the information given, we cannot properly apply the Law of Detachment because there is no direct statement verifying the specific side lengths of rectangle LMNO. For the Law of Detachment to be used correctly, the second statement must directly assert that LMNO has the side lengths in question.
Incorrect Conclusion using Law of Detachment
Given the information provided, we cannot conclude that rectangle LMNO has side lengths of 3 cm and 4 cm just because its area is 12 cm2.