Question

Consider the following theorem. Theorem. Let x be a wamel. If x has been schlumpfed, then x is a borfin. Answer the following questions. (a) Give the converse of this theorem. (b) Give the contrapositive of this theorem. (c) Which statement, (a) or (b), is logically equivalent to the Theorem?

Answer 1

The converse of the theorem is 'If x is a borfin, then x has been schlumpfed.' The contrapositive is 'If x is not a borfin, then x has not been schlumpfed,' which is logically equivalent to the original statement.

Step-by-step explanation:

When considering the given theorem about wamels, we can apply logical operations to construct different related statements. Here's how:

• Converse: This is constructed by reversing the antecedent and the consequent of the given conditional statement. The converse of the theorem would be 'If x is a borfin, then x has been schlumpfed.'
• Contrapositive: This is created by negating both the antecedent and the consequent of the given statement and then swapping them. For the given theorem, the contrapositive would be 'If x is not a borfin, then x has not been schlumpfed.'

Interestingly, the contrapositive is always logically equivalent to the original conditional statement. Therefore, if the original theorem is true, then its contrapositive is also true.

Regarding the SEO questions presented, they are mathematical operations involving equality and multiplication which do not relate directly to the logic operations discussed in the context of wamels, schlumpfing, and borfins.