Dictionary:

disjoint

  (dĭs-joint')

1. To put out of joint; dislocate.
2. To take apart at the joints.
3. To destroy the coherence or connections of.
4. To separate; disjoin.

1. To come apart at the joints.
2. To become dislocated.

Having no elements in common. Used of sets.

[Middle English disjointen, to destroy, ultimately from Old French desjoint, past participle of desjoindre, to disjoin. See disjoin.]

To separate meat at the joint, such as cutting the chicken leg from the thigh.

verb

To become or cause to become apart one from another: break, detach, disjoin, disunite, divide, divorce, part, separate, split (up). Idioms: part company, set at odds. See assemble/disassemble.

Two sets are disjoint if they have no member in common.