Question

1. Prove the validity of the arguments using rules of inference.

  { (p→q) ^ [ q → (r ^ s) ] ^ (p ^ w) ^ [~r v (~w v u) ] } → u

Answer 1

{ (p→q) ^ [ q → (r ^ s) ] ^ (p ^ w) ^ [~r v (~w v u) ] } → u

P is true

q is true

r is true

s is true

W is true

u is true

{ (p→q) ^ [ q → (r ^ s) ] ^ (p ^ w) ^ [~r v (~w v u) ] } → u

${(T\implies T)\land[T\implies (T\land T)]\land (T\land T)\land[\tilde r\cup(\tilde T\cup(\tilde T\cup T)]}\implies u\\ {T \land T\land T\land [F\cup(F \cup T)}\implies T\\ T\land T\land T\land [T]\implies T\\ T\implies T\\$ This is critical row so prove the validity of argument

Using truth table

Lawof syllagism