T5.6 7 of 9

Okay, now lets apply our three step strategy analysis to a more difficult problem. Use derivations to show that...

__D>~B__

(B&C)>~D

**We
may now see how the three strategy steps work for this more complicated example...**

** Start** the Demo.

From the premise 'D>~B'
**deduce** '(B&C)>~D'.

Because (step 1) our (ultimate) goal is to derive '(B&C)>~D',
and (step 2) what to do isn't obvious, *step 3* suggests that we may hope
to **finish** the derivation by means of >I.

Thus, we ** assume** the antecedent of our goal
sentence.

Our plan to use >I provides
us with a *new goal*: we hope to derive the consequent '~D' by line
6 (this is step 1 again).

If it's not obvious what to do next, then *step 3*
again suggests the introduction rule for our goal's main connective: *~I*.
This requires a *second assumption* and a *subderivation within
a subderivation*!

Once again, we have a new goal: to derive *a contradiction*
within the second subderivation.

It may be obvious how to proceed at this point, but if not move to step 3 and apply E-rules (there is no I rule to apply). We should only use E-rules that move toward our goal of a contradiction.

After
line 5, we are able to terminate the second subderivation -- the subderivation
within a subderivation -- lines 3 - 5.

Finally, citing lines 2 through 6, we have shown that if 'B&C' holds, then '~D' does too. Thus, line 7 is justified.

Before moving on, make sure you understand how the strategy steps are utilized
time and again. With a little practice they become very natural.

Replay the demonstration.

Next...

Replay the demonstration.

Next...

MouseOver
thesign to *pause* the demo.