Final answer:
The statement 'Although Paula isn't tired, she neither studies hard nor passes; but Sidney won't study hard and won't pass' can be symbolized using logical notation as a combination of conjunctions and negations to represent the relationships between the variables.
Step-by-step explanation:
The question requires the use of symbolic logic to represent a statement. The statement 'Although Paula isn't tired, she neither studies hard nor passes; but Sidney won't study hard and won't pass' can be symbolized in formal logic. Let's define some variables for the purposes of understanding:
- P for Paula isn't tired
- S for Paula studies hard
- s for Sidney studies hard
- R for Paula passes
- r for Sidney passes
Now, 'although' can be interpreted as a logical conjunction (AND) with a negative clause, and 'neither...nor' as negation (NOT) for both actions. Thus, the first part of the statement can be represented as ~S ∧ ~R (Paula does not study hard and does not pass) despite P (Being untired).
The second part of the statement concerns Sidney and uses 'won't' which is a definite negation, showing both actions do not take place. Therefore, for Sidney, it can be symbolized as ~s ∧ ~r (Sidney will not study hard and will not pass).
Combining both parts, the entire statement could be symbolically represented as P ⇒ (~S ∧ ~R) for Paula, and ~s ∧ ~r for Sidney. This provides a clear representation in logical symbolism of the statements concerning Paula's and Sidney's actions regarding studying and passing.