Question

3. Rewrite each of the following proposition using quantifiers, predicates and variables. Make sure that you clearly define the predicates, variables and domains. There exists a program that gives the correct answer to every question that is posed to it. a. b. For all integers m and n, if m'n is even then either m is even or n is even

Answer 1

a)There exists a program that gives the correct answer to every question that is posed to it

here we define,x is a program,C(x) gives the correct answer to every question when a program x is posed to it.

      ∃x(C(x))

b)For all integers m,n,if m*n is even then either m is even or n is even

F(x,y)=x,y such that x*y is even

C(X)=x is even

∀m∀n F(m,n)∃(C(m)vC(n)).