ONLY 4TH Question is needed, 1st is attached only for reference EVEN SOLUTION FOR 1 IS ATTACHED

4. (a) Is the sequence of symbols "P= M" a well-formed formula of predicate logic, using the "Possible Missions" domain of discourse from question 1? Explain why or why not. (b) Consider the set of predicate logic sentences we can write about the "Possible Missions" domain. Is this set finite; infinite but countable; or not countable? Explain your answer. (c) Let S be the set of predicate logic sentences from question 4(b). Suppose we take the union of S and the real numbers, R. Is SUR countable or uncountable? Explain your answer. 1. Consider the following domain of discourse. THE "POSSIBLE MISSIONS DOMAIN Let the constant m mean "the current mission". Let the predicate M(2) mean "ris a mission", and the predicate PC mean "ris possible". We will call this the "Possible Missions" domain. Give predicate logic formulas for the following English sentences about the Possible Missions domain of discourse. (Make sure you add sufficient paren- theses to give the meaning you intend.) (a) m is not a possible mission. (b) If m is possible, any mission is possible, (c) If nothing is possible, m is possible. (a m is not a possible mission. N (Mm) n pem)) 6 If n is pcm) possible any mission is possible Vin (Mm) AP (m) If nothing P(m) is possible (m) m is possible 4. (a) Is the sequence of symbols "P= M" a well-formed formula of predicate logic, using the "Possible Missions" domain of discourse from question 1? Explain why or why not. (b) Consider the set of predicate logic sentences we can write about the "Possible Missions" domain. Is this set finite; infinite but countable; or not countable? Explain your answer. (c) Let S be the set of predicate logic sentences from question 4(b). Suppose we take the union of S and the real numbers, R. Is SUR countable or uncountable? Explain your answer. 1. Consider the following domain of discourse. THE "POSSIBLE MISSIONS DOMAIN Let the constant m mean "the current mission". Let the predicate M(2) mean "ris a mission", and the predicate PC mean "ris possible". We will call this the "Possible Missions" domain. Give predicate logic formulas for the following English sentences about the Possible Missions domain of discourse. (Make sure you add sufficient paren- theses to give the meaning you intend.) (a) m is not a possible mission. (b) If m is possible, any mission is possible, (c) If nothing is possible, m is possible. (a m is not a possible mission. N (Mm) n pem)) 6 If n is pcm) possible any mission is possible Vin (Mm) AP (m) If nothing P(m) is possible (m) m is possible