Negation/Contrapositives of "Unless" statements

[mtariq]

Hi, could someone help me out with clearly understanding "unless" statements? I just realized that I don't fully grasp this concept after reviewing some drills in Lesson 2 and Lesson 5. How do you know when the logical opposite (same as contrapositive, correct?) of a statement is "might be" vs "will not be"? For example:

Lesson 1 has a statement that says: We cannot win the war unless we receive additional supplies.

Diagram: Win->Receive additional supplies
Contrapositive: do NOT receive additional supplies-> do NOT win

Lesson 5 has a statement that says: Happiness is impossible unless we profess a commitment to freedom.

I would diagram this statement like this: Happiness NOT impossible->profess a commitment to freedom
Contrapositive: do NOT profess a commitment->happiness impossible
The answer though, says: Even if we do not profess a commitment to freedom, happiness may still be possible.

I think what I'm missing is that the second statement builds on the knowledge in Lesson 2, so technically, the correct answer for the first statement would include could be true terms as well? Or am I totally missing the mark?

-Maria

[Dave Killoran]

Hi Maria,

Thanks for the question. This is a pretty simple one to answer, fortunately

In Lesson 2, the drill is asking for the correct conditional diagram of the statement.

In Lesson 5, the drill is asking for the negation of the statement. Thus, that changes the answer key significantly.

So, you are correct in stating what the conditional diagram would be in the Lesson 5 question; the answer key then shows you the negation of that statement.

Please let me know if that helps. Thanks!

[mtariq]

Oh, ok! So I didn't realize the difference between conditional diagramming (taking the contrapositive) and negation (taking the logical opposite).

[Dave Killoran]

No problem!

Just a note: conditional diagramming is just the representation of a conditional statement in arrow form; the contrapositive is part and parcel of that.

The logical negation of a statement just produces its opposite, and so the original statement could be conditional, but it doesn't have to be. In the one you cited, it just happened that the original statement was conditional

Thanks!

[mtariq]

Got it! Thank you