a Rewrite the given information as conditionals and apply the Law of Detachment.
B
b Apply the Law of Syllogism.
A
a Ben
B
b Andrea, Claire and Ben
Practice makes perfect
a We have been given the following statements.
Statement I: Claire reads anything Andrea reads.
Statement II: Ben reads what Claire reads.
Statement III: Claire reads what Ben reads.
Statement IV: Andrea reads whatever Dion reads.
Let's write these statements as conditional and biconditional statements.
Statement I: If Andrea reads a book, then Claire reads the book.
Statement II: If Ben reads a book, then Claire reads the book.
Statement III: If Claire reads a book, then Ben reads the book.
Statement IV: If Dion reads a book, then Andrea reads the book,
We know that Claire is reading Hamlet, which matches the hypothesis of Statement III. Therefore, we can use the Law of Detachment to make a conclusion.
If p → q &is true
and p &is true,
then q &is true.
Let's apply the Law of Detachment.
Conclusion
Ben is reading Hamlet.
b Let's use the Law of Syllogism between Statement I and III, since the conclusion of Statement II matches the hypothesis of Statement III as the following.
If p → q &is true
and q → r &is true,
then p → r &is true.
Applying the Law of Syllogism we have the following conclusion.
Conclusion
If Andrea reads a book,
then Ben reads the book.
As a result, we can say that If Andrea is reading King Lear, then Claire and Ben are also reading King Lear. However, we cannot make any comment about Dion's book.
