Comment

Comment by Katrina J. Combs on January 7, 2012 at 11:00pm

Ty and William: Thanks for your thoughts!  These are helpful!

Comment by William Carey on January 7, 2012 at 7:24pm

It is vexing that English combined vel and aut... One strategy you might try is teaching them another symbol for exclusive or and its associated truth table. Each time you see "or" in English, you can ask them whether it's inclusive or exclusive, and use the appropriate truth table. If exclusive or never shows up on assignments from the book, who'd ever know?

(XOR is worth knowing, as it shows up in computer science all over the place!)

Comment by Ty Rallens on January 6, 2012 at 1:13am

I've also seen that the inclusive OR is a difficult concept. In everyday speech we default to an exclusive meaning of the word "or" so inclusive is counterintuitive. I have tried to illustrate the technique by coming up with examples that are not exclusive, like "James Madison was a president or he was an architect of the U.S. Constitution." Logically, this is a true statement, even though it sounds strangle in normal English. Likewise, even thoug "Cicero was a Greek or he was a slave." is false, this is an inclusive OR because there's nothing that prevents a Greek from also being a slave.

As for symbolic logic, it might be helpful to compare the behavior of the OR symbol to the commutative property in mathematics. Just as 4+2 = 2+4, so A V B (using 'V' for the OR symbol) is logically equivalent to B V A.

Comment by Katrina J. Combs on January 5, 2012 at 11:42pm

To clarify: The struggle comes when they realize there are multiple ways to write out the statement in symbolic form.

Comment by Katrina J. Combs on January 3, 2012 at 7:31pm

My 8th grade students really struggle with the inclusive or (vel).  It's an onging issue.  We always come back to our examples we devised for ourselves: "We offer paper or plastic; we take cash or check."  (Of course, a store offers both paper and plastic, but the customer chooses one; the cash or check example is similar.)  So they understand it in theory, but when we apply it in symbolic logic, it gets disastrous.  Help!!  Any ideas?