Every valid argument with true premises has a true conclusion. Rewrite the above statement in the form V[x] x, if [y] then [z] (where each of the second and third blanks are sentences involving the variable x) :

Let y (x) = "x is valid and x has true premises" and z (x) = "x has a true conclusion".

Step-by-step explanation:

The universe U is the collection of all arguments so that x∈U. The statement uses the universal quantifier ∀ represented by the word "Every". The words "valid", "with true premises" and "has a true conclusions" are properties of an argument x.

We can interptet the statement as: "For all x, (x is valid and x has true premises) → (x has a true conclusion) ". Symbolically, (∀x) (y (x) →z (x)). The implication → can be read as "if y (x) then z (x) ".