Question 1: Predicate Logic 14 points) The domain for the variables x, y and z is the set of all people, the domain for the variablet is the set of all cities. Let us be given propositional functions with the following meaning I(2,t): "x is in t", F(2,y): "r and y are friends", M(x,y): "x met y", C(2): " is a celebrity". (a) Write a formula to express the sentence "A person in Madrid is known by everyone in Luanda only if this person is a celebrity.". [2 points) (No justification is needed. Use only predicates and variables, which are defined in the above problem formulation.) (b) Write a formula to express the sentence "There is a person in New Delhi, who met every celebrity from London.". (2 points) (No justification is needed. Use only predicates and variables, which are defined in the above problem formulation.)