Translation of the statement : Some Computer Science courses are not being taken by any Mathematics Major where M(x) is the statement x is a Mathematics Major, C(y) is the statement y is a Computer Science course, and T(x,y) is the statement is x taking y. Assume that the universe for x is the set of all students and the universe for y is the set of all course Step 1. We want to represent both the left hand side and right hand side of are by predicates or propositional functions: The left hand side of are: Some courses are Computer Science courses The right hand side of are: course is not being taken by any Mathematics Major Step 2. Break right hand side of are by 2 predicates or propositional functions: The left hand side of are: Some courses, the course is a Computer Science course The right hand side of are: any student, the student is a Mathematics Major course is not being taken by the student Step 3. Represent each piece in Step 2 by symbols. For the left hand side of are: Take out quantifier some and replaced by 3 and using variable y then we have using symbols: (use variable y and propositional function Cy)) For the Left Hand Side, LHSAns: For the right hand side of are: Take out quantifier any and replaced by V and using variables x & y, then we have using symbols: (use variables x.y and propositional functions Mix) and T(x,y)) For the Right Hand Side, RHSAns: to combine those 2 pieces on the right hand side in Step 3, we have Step 4: Use Rule V and For the Right hand side: RHSAns: Step 5: Use Rule 3 and to combine the LHSAns in Step 3 and RHSAns in Step 4 by putting RHSAns in (), such as (LHSAns (RHSAns)), we get (You may rearrange the parenthesis to make sense) Ans: Translation of the statement : Some Computer Science courses are not being taken by any Mathematics Major where M(x) is the statement x is a Mathematics Major, C(y) is the statement y is a Computer Science course, and T(x,y) is the statement is x taking y. Assume that the universe for x is the set of all students and the universe for y is the set of all course Step 1. We want to represent both the left hand side and right hand side of are by predicates or propositional functions: The left hand side of are: Some courses are Computer Science courses The right hand side of are: course is not being taken by any Mathematics Major Step 2. Break right hand side of are by 2 predicates or propositional functions: The left hand side of are: Some courses, the course is a Computer Science course The right hand side of are: any student, the student is a Mathematics Major course is not being taken by the student Step 3. Represent each piece in Step 2 by symbols. For the left hand side of are: Take out quantifier some and replaced by 3 and using variable y then we have using symbols: (use variable y and propositional function Cy)) For the Left Hand Side, LHSAns: For the right hand side of are: Take out quantifier any and replaced by V and using variables x & y, then we have using symbols: (use variables x.y and propositional functions Mix) and T(x,y)) For the Right Hand Side, RHSAns: to combine those 2 pieces on the right hand side in Step 3, we have Step 4: Use Rule V and For the Right hand side: RHSAns: Step 5: Use Rule 3 and to combine the LHSAns in Step 3 and RHSAns in Step 4 by putting RHSAns in (), such as (LHSAns (RHSAns)), we get (You may rearrange the parenthesis to make sense) Ans
