Logical operations in modal three-valued logic (XOR, IMP EQV)

Question

From my understanding, the modal quantifier possibly relaxes the behaviour of logical conjunction:

(true)                and (possibly false)   => true
(true)                and (possibly unknown) => true
(possibly true)       and (possibly false)   => true
(possibly true)       and (possibly unknown) => true
(necessarily true)    and (possibly false)   => true
(necessarily true)    and (possibly unknown) => true
(unknown)             and (possibly false)   => unknown
(possibly unknown)    and (possibly false)   => unknown
(necessarily unknown) and (possibly false)   => unknown

My question is: does it have any specific impact on other operations (like exclusive disjunction, implication and equivalence)? What about these examples (which can't figure out myself):

(true) xor (possibly true)    => true | false   ?
(true) xor (possibly unknown) => true | unknown ?