[SOLVED] Ve492- homework 9

We ask a logician (who only tells the truth) about his sentimental life, and he answers the following two statements:What can we conclude? Answer the following questions by ”yes”, ”no”, ”unsure”.Which of the following are correct?that includes A,B,C.1a,b,c,dWe denote L0 the set of propositional logic sentences built from a set X of n propositional symbols. we consider the following new formal languages, where some logical connectives are not allowed: • L1 is defined as follows:True and False are sentences of L1. All symbols of X are sentences of L1. If s,s⁰ are two sentences of L1, then ¬s, (s ∧ s⁰), (s ∨ s⁰), and (s ⇒ s⁰) are four sentences of L1. • L2 is defined as follows:True and False are sentences of L2. All symbols of X are sentences of L2. If s,s⁰ are two sentences of L2, then ¬s, (s ∧ s⁰), and (s ∨ s⁰) are three sentences of L2. • L3 is defined as follows:True and False are sentences of L3. All symbols of X are sentences of L3. If s,s⁰ are two sentences of L3, then ¬s and (s ∧ s⁰) are two sentences of L3. • L4 is defined as follows:True and False are sentences of L4. All symbols of X are sentences of L4. If s are two sentences of L4, then ¬s is a sentence of L4.We consider the following binary relation between languages: L ⊆ L’ iff any sentences that can be expressed in L can equivalently be expressed in L’.Answer ”yes” or ”no” the following questions.Are the following are valid (necessarily true) sentences?Answer ”Valid” or ”Invalid” the following questions.Valid,Valid,ValidThis exercise uses the function Map Color and predicates In(T,y), Borders(x,y), and Country(x), whose arguments are geographical regions, along with constant symbols for various regions. In each of the following we give an English sentence and a number of candidate logical expressions.(iv) ∀c Country(c) ∧ Border(c,Ecuador) ∧ In(c,SouthAmerica).For each of the logical expressions, state whether it…233233312221333