: Logic, Predicates and Quantified Statements

a$)$ Consider the claim, $"$If a student studies diligently, then they will score well on exams." Express this claim as a logical conditional statement. Then, brainstorm and discuss potential risks if the converse, inverse, or contrapositive statements are assumed to be true in the context of academic performance and student success. For your symbolic representation, consider p: $$student studies diligently$$ and q: $$student scores well on exams$.$

b$)$ Explain the difference between a statement that is universally quantified and one that is existentially quantified. Give an example of each.

c$)$ Consider the claim, $$If a user enters a correct password, then access is granted.$$ Express this claim as a logical conditional statement and explain the potential security risks if the converse, inverse, or contra$-$ positive statements are implemented instead.