Final answer:
The truth values of logical expressions depend on the known truths of variables; expressions can be true, false, or unknown. In probability, the complementary nature of the success probability p and failure probability q plays a key role. Logical expressions are used to formalize arguments and to outline the behavior of probabilities in repeated trials.
Step-by-step explanation:
Understanding Logical Expressions
The given variables are p is true, q is false, and the truth value for variable r is unknown. Answering questions about the truth value of logical expressions depends on the operations involved and the known variables.
1) When a statement is simply true, its truth value is immediately true. Therefore, any expression that evaluates to true is true.
2) Conversely, an expression that evaluates to false has a truth value of false.
3) If an expression's outcome is dependent on an unknown variable, in this case r, the overall truth value of the expression would be unknown. This holds unless other parts of the expression determine the outcome regardless of the unknown variable.
In probability theory, specifically in a Bernoulli trial, the probability p represents the chance of success, and q represents the chance of failure, such that p + q = 1 as they are complementary probabilities. If q is known, then p can be found by subtracting q from 1.
Expressing arguments in logical form, such as P > Q means 'if P then Q'.
When we consider probability in repeated trials, the statement that the probability of success p and the probability of failure q do not change from trial to trial aligns with the concept of a fixed probability in repeated Bernoulli trials. This is evidence in the constant probability of rolling a specific number with a fair die.