Lesson 7, page 42-Negating Conditional Statements

[bbenditz]

On the Concept overview drill in lesson 7 page 42, it asks you to Logically negate the statement "The councilman cannot speak, unless the mayor allows his name to appear on the list." I though that when logically negating conditional statements only the necessary condition needs to be negated, but the answer says that both the sufficient and necessary should be negated in this case. Do both the sufficient and necessary always get negated when there is "Except of Unless" in the conditional statement?

[Steve Stein]

Thanks for your question. The point of that explanation was that, no matter how you choose to rephrase the conditional statement, in the negated version you end up denying the necessity of the "necessary" condition.

So, the statement that requires negation is as follows:
The councilman cannot speak unless his name is allowed on the list on the list.

According to the statement above, what is the necessary condition? the name on the list. So, how do we negate that statement? By saying, "No, that's not necessary."

As the explanation says, we could word this negated version as:

"It is not necessary that the name be allowed on the list for the councilman to speak"

or as:

"The councilman can speak even without his name allowed on the list."

Either way, the negated version of the question denies the necessity of the original necessary condition (his name being allowed on the list).

Tricky--let me know whether that clears it up--thanks!

~Steve

[mbrefo]

I also have a question regarding this drill. I thought in the book it stated that when unless, except, and without are used:
1. the term modified by unless, except, etc becomes the necessary condition,
2. then the remaining term is negated then becomes the sufficient

I'm confused as to how the necessary is now the one that becomes negated when the book stated the sufficient becomes negated.

Similar to lesson 5 pg. 5-29 question 4. Unless modifies "we profess a commitment to freedom." However, it becomes the sufficient not the necessary and it is negated.

Can you please clarify the proper use of negation with unless, except uses in negation conditional statements and how it applies to both the question in lesson 7 pg 42 and 5-29 question 4?

[KelseyWoods]

Hi mbrefo!

You are correct that to diagram a conditional statement with "unless," "until," "except," or "without" the term modified by those words becomes necessary and the remaining term is negated before it becomes sufficient. Both the question on 7-42 and the question on 5-29, however, are asking you to take an additional step by negating the conditional statement, as you would if you were trying to apply the Assumption Negation Technique to a conditional answer choice.

So to diagram the 5-29 statement ("Happiness is impossible unless we profess a commitment to freedom"), we would follow the two-step Unless Equation and our diagram would look like this:

Happiness possible we profess a commitment to freedom

Next, we need to negate that entire conditional statement. To negate a conditional statement, you just need to show that the necessary condition is not actually necessary. In this case, then, the negation would be that happiness may be possible even if we do not profess a commitment to freedom. That's where the answer in the back of the book comes from.

The same holds true for the statement on page 7-42. The diagram of the conditional statement would look like this:

Councilman speaks mayor allows his name on the list

When we negate that conditional statement, we show that the councilman can speak even if the mayor does not allow his name on the list.

Hope this helps!

Best,
Kelsey

[mbrefo]

This makes sense!!! Thanks so much!