If some arguments of the form disjunctive syllogism have false premises, then some arguments with false premises are deductively valid. Some arguments of the form disjunctive syllogism have false premises. So some arguments with false premises are deductively valid.
This argument is valid but unsound.
Is the above statement true?
There is perhaps a hidden premise that all arguments of the form disjunctive syllogism are valid. That said,
"If some arguments of the form disjunctive syllogism have false premises, then some arguments with false premises are deductively valid" is true,
"Some arguments of the form disjunctive syllogism have false premises" is true, and
"Some arguments with false premises are deductively valid" follows by modus ponens.
This would suggest that your argument is both valid and sound. There is one little catch, however. You say "false premises" plural. If by this you mean an instance of disjunctive syllogism both of whose premises are false, then this is not possible. Disjunctive syllogisms have the form A or B; not A; therefore B. For the first premise to be false, A must be false, and hence the second premise is true. If that is your intended meaning then "Some arguments of the form disjunctive syllogism have false premises" is false, and so the argument would not be sound.
