Select the correct relationships between various AI fields:

a$)$ machine learning is a subtield of deep learning and deep learning is a field of $Al$

b$)$ deep learning is a subfield of machine learning and machine learning is a field of $Al$

c$)$ pattern recognition is a subfield of machine learning and machine learning is a field of $Al$

d$)$ big data is a field of deep learning, and deep learning is a subfield of machine learning

e$)$ Bayesian networks is a field of probabilistic reasoning and probabilistic reasoning is a field of propositional logic