Logic Game Challenge #34: Party Problem (Hard)

[JianiL759]

Could anyone please help with me with Q6? Answers B and C both contain Lance, but if all four women come to the party how can Lance be present considering that if both he and Reena come Tracy won't come?

[Laura Damone]

First, sorry for the delayed response here. Amidst all the chaos of the last week, this one slipped through the cracks.

Second, it looks like you accidentally reversed the Lance Tracey Reena rule. The rule tells us that Tracey is coming unless both Lance and Reena come. The best way to diagram a compound "unless" statement (as in, an "unless" statement with an "and" or an "or"), is to think about drawing the arrow through the word "unless." The word "unless" will introduce the necessary condition(s). The other part of the statement, negated, becomes the sufficient condition.

That give us this:

- Tracey --> Lance and Reena

And the contrapositive:

- Lance or - Reena --> Tracey

Notice we had to change the "and" to "or" when we contraposed. You will always do this when you contrapose a compound conditional statement.

With the rule properly diagrammed, you can see that Lance and Reena don't force Tracey out.

The reason that C is impossible and therefore correct is that it contains both Lance and Oscar. Rule # 2 tells us that if Oscar and Pam come, Lance won't:

Oscar + Pam --> - Lance

And the Contrapositive:

Lance --> - Oscar or - Pam

Again, notice that we switched the "and" to "or" when we contraposed.

So, if all four women are at the party, Pam is in for sure. That means if Oscar is in, it triggers the rule and kicks Lance out. If Lance is in, it triggers the contrapositive, and since Pam can't get kicked out, Oscar gets the boot. You can't have Oscar and Lance together at any party Pam attends.

Hope this helps!

[JianiL759]

First, sorry for the delayed response here. Amidst all the chaos of the last week, this one slipped through the cracks.

Second, it looks like you accidentally reversed the Lance Tracey Reena rule. The rule tells us that Tracey is coming unless both Lance and Reena come. The best way to diagram a compound "unless" statement (as in, an "unless" statement with an "and" or an "or"), is to think about drawing the arrow through the word "unless." The word "unless" will introduce the necessary condition(s). The other part of the statement, negated, becomes the sufficient condition.

That give us this:

- Tracey --> Lance and Reena

And the contrapositive:

- Lance or - Reena --> Tracey

Notice we had to change the "and" to "or" when we contraposed. You will always do this when you contrapose a compound conditional statement.

With the rule properly diagrammed, you can see that Lance and Reena don't force Tracey out.

The reason that C is impossible and therefore correct is that it contains both Lance and Oscar. Rule # 2 tells us that if Oscar and Pam come, Lance won't:

Oscar + Pam --> - Lance

And the Contrapositive:

Lance --> - Oscar or - Pam

Again, notice that we switched the "and" to "or" when we contraposed.

So, if all four women are at the party, Pam is in for sure. That means if Oscar is in, it triggers the rule and kicks Lance out. If Lance is in, it triggers the contrapositive, and since Pam can't get kicked out, Oscar gets the boot. You can't have Oscar and Lance together at any party Pam attends.

Hope this helps!

Oh I see. Thank you so much!