Question

Rewrite the following statement in the form ∀x ______, if _______ then _______ (where each of the second two blanks are sentences involving the variable x) Every valid argument with true premises has a true conclusion.

Answer 1

"Vx: if x is a valid argument with true premises then x has a true conclusion"

In a symbol form

Vx ( P(x) ⇒ 2(x) )

Explanation:

The Following statement in the form ∀x ______, if _______ then _______ is a valid argument and this because any valid argument with "true premises" has a "true conclusion" as well

we will rewrite this statement in a universal condition statement form

assume x is a valid argument with true premises

then the following holds true

p(x) : x is a valid argument with true premises

q(x) : x has true conclusion

applying universal conditional statement

"Vx, if x is a valid argument with true premises then x has a true conclusion"

In a symbol form

Vx ( P(x) ⇒ 2(x) )