$5\mathrm{.}1$ Explain predicate calculus and its significance in AI$.$ Describe the differences between propositional logic and predicate logic. Provide examples to illustrate your explanation. $(10$ Marks$)$

$5\mathrm{.}2$ Given the following statements, construct the corresponding predicate calculus expressions and explain your reasoning:

$1.$ All students are required to take exams.

$2.$ Therefore, Kepler is required to take exams.

$3.$ Every car has an engine.

$4.$ Every programmer knows a programming language. John is a programmer. Therefore, John knows a programming language $(10$ Marks$)$