12. Write expressions for the following in Predicate Logic (defining your predi- cates) and then determine if the inference is valid. If it is, you must indicate the rules used. If it is invalid you must indicate why. Doug, a student in this class, knows how to program in Java. Everyone who knows how to program in Java can get a high-paying job. Therefore, someone in this class can get a high-paying job.

Mathematical Logic. First-order or predicate logic. Exercises on structures and models. 1. Prove that: ₁ \v₂Qv₂ [[c²]] iff ₁ €₂ Where Q is a two-argument predicate symbol and c is a constant symbol. Please be as clear as possible. Show and explain all the steps of the proof. Thank you very much.

State our definition of “valid inference” and then explain how to use a truth table to test the validity of an inference in zeroth-order logic.

A local health clinic often makes this statement to its patients. If you get a flu shot, then you won't get the flu thus winter. (a) Statements p and q are defined as follows. p: You get a flu shot. q: You get the flu this winter. Write the clinic's statement in symbolic form using p and q Symbolic form: __ (b) Suppose the following situation occurred. You got a flu shot. During winter, you got flu. Complete the table to determine the truth of the clinic's statement in this situation. Use T for true and F for false.

Propositional wffs and truth tables belong to a system of two-valued logic because everything has one of two values, F or T, which we can think of as 0 or 1. In fuzzy logic, or many-valued logic, statement letters are assigned values in a range between 0 and 1 to reflect some “probability” to which they are false or true. A statement letter with a truth value of 0.9 is “mostly true” or “has a high probability of being true” while a statement letter with a truth value of 0.05 “has a very high probability of being false.” Fuzzy logic is used to manage decisions in many imprecise situations such as robotics, manufacturing, or instrument control. Truth values for compound statements are determined as follows.A′ has the truth value 1 − A.A Λ B has the truth value that is the minimum of the values of A and of B.A ∨ B has the truth value that is the maximum of the values of A and B.a. Explain why these are reasonable assignments for the truth values of A′, A Λ B, and A ∨ B.Suppose the…

Which of the following is the converse of the conditional statement: If you were bitten by a waglygrill, then you need to drink the Jubey sauce.

the course is (discrete structure) you need to match A,B,C

Translate into predicate logic and show the logical computation of the negation of the statement: No duck talks or all ducks squawk. Give a key for your predicate. Additionally, give the negation of the statement in simple English.

Translate the given statement into symbolic form. Be sure to define all pred- icates used. Use the variable a with domain D = {a : a is an animal } as your main variable. Then, negate the symbolic statement. In your answer, negations should appear only in front of predicates. Finally, rewrite the negated statement clearly in plain English. "Any animal that is wild can be tamed." 2.

please answer Q5 only, thanks.