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Old English hatian "to hate," from Proto-Germanic *hatojanan (cf. Old Saxon haton, Old Norse hata, German hassen, Gothic hatan "to hate"), from PIE root *kad- "sorrow, hatred" (cf. Avestan sadra- "grief, sorrow, calamity," Greek kedos "care, trouble, sorrow," Welsh cas "pain, anger"). Related: Hated; hating. French haine (n.), hair (v.) are Germanic. Hate crime attested from 1988.
Old English hete "hatred, spite," from Proto-Germanic *hatis- (cf. Old Norse hattr, Old Frisian hat, Dutch haat, Old High German has, German Hass, Gothic hatis; see hate (v.)). Altered in Middle English to conform with the verb. Hate mail is first attested 1967.