Mathematical logic and formal semantics questions.

Find Mathematical logic and formal semantics university examination questions in acaproso.com

#	Question
1	Detrmine the truth value of each of the following statements if the universe of each variable consists of all real numbers all integers Justify your answers. $exists xexists y(x+y eq y+x)$ $forall x exists y(x+y=2wedge 2x-y=2)$ Mathematical Calculation
2	Describe the proof by resolution technique Mathematical Calculation
3	Use resolution to prove the following $(^-pvee t),(^-qvee s),(^-rvee t),(p vee qvee rvee u)vdash (svee tvee u).$ $(^-rvee u),(^-uvee ^-w),(rvee^-w)vdash w.$ $(pvee ^-q),(^-wvee q),(wvee qvee r), ^-pvdash r.$ $(tvee ^-evee d),(^-tvee c),((ewedge ^-g)vee ^-dvee p), (tvee cvee ^-d vee g),\ (^-pvee ^-g),^-cvdash ^-(dwedge e).$ Mathematical Calculation
4	Explain the disadvantages of using the truth table method in testing proposal satisfiability. Mathematical Calculation
5	Explain how the semantix tableaux method can be used to test the validity of a proposition. Mathematical Calculation
6	Use the semantic tableaux to test satisfiability of the following proposals $^-(p ightarrow q)wedge(^-pvee q)$ $(pvee ^-q)wedge(qwedge ^-r)wedge(r ightarrow p)$ $[(p ightarrow(^-q ightarrow r))wedge(p ightarrow^-q)] ightarrow(p ightarrow r)$ Mathematical Calculation
7	Give proof of the following statements. For each statement, state a type of the proof used. For every real number x, if $x^2 +1<0$ then $x^5>4$ For every real number x, if $x>0$ then $x^2 +5 >0$ Mathematical Calculation
8	Show by giving a direct proof , that the square of an odd number is odd. Mathematical Calculation
9	Show , by giving an indirect proof, that if $x^2$ is divisible by 3 then x is also divisible by 3. Mathematical Calculation
10	Show by giving a proof by contradiction , that $sqrt3$ is irrational. Mathematical Calculation