The knowledge-based system CUSTOMER contains the following list of basic facts.

Note that expiring(x) means that xs subscription will expire at the end of the month; trial(x) means that x is subscribed to a free trial; basic(x) means that x is a basic feature; premium(x) means that x is a premium feature; and subscription(x,y) means that xs subscription includes feature y.

(a) Answer the following formal queries, briefly justifying your answers. i. ? - expiring(c) and subscription(c, ad-free) ii. ? - subscription(Smith, f ) and (not subscription(c, f )) iii. ? - expiring(c) and premium( f ) and subscription(c, f ) iv. ? - subscription(c, downloads) and (subscription(c, multi-screen) or subscription(c, 4K))

(b) Write down formal queries asking each of the following. i. Do the customers Williams and Hodge have any common features on their subscriptions? ii. Is there a customer whose subscription is expiring and does not include downloads?

(c) Give inference rules to define the following new predicates. i. highuse(c) to mean that cs subscription includes the premium features multi-screen and 4K ii. samepremium(c, d) to mean that both cs and ds subscription includes the same premium feature

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The topic of this maths question is Applications in Math, also known as Knowledge based systems in Mathematics for computing.

expiring(Smith) basic(watchlist) subscription(Williams, watchlist) expiring(Newman) basic(downloads) subscription(Williams, downloads) expiring(Hodge) subscription(Williams, ad-free) premium(ad-free) subscription(Smith, watchlist) trial(Jones) premium(multi-screen) subscription(Smith, downloads) premium(4K) subscription(Smith, multi-screen) subscription(Newman, downloads) subscription(Hodge, watchlist) subscription(Hodge, ad-free) subscription(Hodge, multi-screen) subscription(Jones, ad-free)