Given ∀x.(p(x) ∧ q(x)), use the Fitch System to prove ∀x.p(x) ∧ ∀x.q(x).
To apply a rule of inference, check the lines you wish to use as premises and click the button for the rule of inference. Reiteration allows you to repeat an earlier item. To delete one or more lines from a proof, check the desired lines and click Delete. When entering expressions, use Ascii characters only. Use ~ for ¬; use & for ∧; use | for ∨; use => for ⇒; use <=> for ⇔; use A for ∀; use E for ∃; and use : for . in quantified sentences. Also, for variables use strings of alphanumeric characters that begin with a capital letter. For example, to write the sentence ∀x.∃y.(p(x) ∧ q(y) ⇒ r(y)∨¬s(y)), write AX:EY:(p(X)&q(Y)=>r(Y)|~s(Y)).
Enter the premise you wish to add to the proof:
Enter the assumption you wish to make:
Enter the conclusion you wish to add to the proof:
Enter the justification for this conclusion:
Enter the sentence you wish to disjoin to the checked items: