LR Biconditional Reasoning Inference

[ChicaRosa]

I just encountered a biconditional statement where one variable is negated and I'm not sure how to go about it?

Ex: Beetlejuice will go to the party if and only if the Sandworm doesn't go.

Diagram: B S, Contrapositive: S B

Would this be the correct diagram for the statement and it's contrapositive?

Would these be the correct inferences from below ?

1. Beetlejuice can go but the Sandworm can't attend.

2. The Sandworm goes to the party but Beetlejuice doesn't go to the party

Thank You!

[Nikki Siclunov]

Hi ChicaRosa,

Thanks for the question.

A bi-conditional statement where one condition is negated can be diagrammed as follows:

• • B S
    S B (contrapositive)

Essentially, "B if and only if not-S" is logically identical in meaning to "S if and only if not-B". Test-makers can present the same relationship in several different ways:

• B if and only if not-S
  S if and only if not-B
  Exactly one of S or B attends
  Either S attends without B, or else B attends without S
  Either B or S, but not both, must attend

All of these entail the same exact inferences you mention in your post: either S but no B, or else B but no S.

Check out my Conditional Reasoning Cheat Sheet when you get a chance :

Thanks,