Let's analyze the definition and answer the questions to decide whether it is good!
A ligament is a band of tough tissue connecting bones or holding organs in place.
Can you write the statement as two true conditionals?
Let's write the two conditionals we can form from this statement. In the first one the hypothesis will be that a ligament is a band of tough tissue, and the conclusion will be that then it connects bones or holds organs in place. We will reverse this to get the second conditional.
If a band of tough tissue is a ligament, then it connects bones or holds organs in place.
If a band of tissue connects bones or holds organs in place, then it is a ligament.
Are both of them true? The first one definitely is, because it matches with the statement. However, notice that a skull also holds organs in place, but it is not a ligament. Therefore, the second conditional is not true.
Are the two true conditionals converses of each other?
Let's review the definition of a converse first!
Conditional
Converse
p → q
q → p
As we can see, the converse is just reversing the places of the hypothesis and the conclusion. This is the case in our conditional statements, so they are converses of each other. However, we already know that not both of them are true.
Is the definition good?
We know that a definition is good if it can be written as a true biconditional. A biconditional, however, is a single true statement that combines a true conditional and its true converse. Since our converse is false, then we can conclude that the biconditional will also be false. Therefore, this definition is not true.
