As indicated by answers to [Can “whose” refer to an inanimate object?][1] on ELU, some people wouldn't be happy with OP's use of it here. I'm not one of them, and given how awkward it would be to avoid the word in OP's construction, I'd just ignore those pedantic prescriptivist grammarians who say it's wrong. Note specifically [Peter Shor's answer][2] on that ELU question, with several examples of Shakespeare using *whose* to indicate association with inanimate objects. [Here][3] are many thousands of written instances of *"equations **whose** solutions"*, which is perfectly normal English. By the same token, there's nothing wrong with OP's *...sets of elements whose pairs...* --- Having (I hope) dismissed criticism of *whose*, I'd say that most native speakers would use *every* rather than *each* in OP's particular sentence. I know I said in [another answer][4] that using *every* in this way is usually a bit *stylised/dated*. But here it's just "formal", which is appropriate in a "mathematical" context. I can't exactly *explain* why *"every"* is better than *"each"* here, and I very much doubt it involves any "grammatical rule". But to support my contention that it *is* "better"... > [whose **each** response][5] (0 hits in Google Books) > [whose **every** response][6] (142 hits) I'll just add that the corresponding figures for ["whose each/every **pair**"][7] are 3/116, and for [...**solution**][8] they're 5/27, which may suggest that mathematicians are less attuned to such subtle distinctions. [1]: http://english.stackexchange.com/questions/23541/can-whose-refer-to-an-inanimate-object [2]: http://english.stackexchange.com/a/23546/2637 [3]: https://www.google.co.uk/search?q=%22equation%20whose%20arguments%22&btnG=Search%20Books&tbm=bks&tbo=1#hl=en&tbo=d&tbm=bks&sclient=psy-ab&q=%22equations%20whose%20solutions%22&oq=%22equations%20whose%20solutions%22&gs_l=serp.3...81771.81771.1.82232.1.1.0.0.0.0.69.69.1.1.0...0.0...1c.1.2.serp.mwD6u3snn4w&pbx=1&bav=on.2,or.r_gc.r_pw.r_cp.r_qf.&bvm=bv.42261806,d.d2k&fp=444189726e5cb09f&biw=1415&bih=825 [4]: http://english.stackexchange.com/a/103887/2637 [5]: https://www.google.co.uk/search?q=%22equation%20whose%20arguments%22&btnG=Search%20Books&tbm=bks&tbo=1#hl=en&tbo=d&tbm=bks&sclient=psy-ab&q=%22whose%20each%20response%22&oq=%22whose%20each%20response%22&gs_l=serp.3...24833.29296.7.30422.16.16.0.0.0.0.115.1228.14j2.16.0...0.0...1c.1.2.serp.B4THzLr449I&pbx=1&bav=on.2,or.r_gc.r_pw.r_cp.r_qf.&bvm=bv.42261806,d.d2k&fp=444189726e5cb09f&biw=1415&bih=825 [6]: https://www.google.co.uk/search?q=%22equation%20whose%20arguments%22&btnG=Search%20Books&tbm=bks&tbo=1#hl=en&tbo=d&tbm=bks&sclient=psy-ab&q=%22whose%20every%20response%22&oq=%22whose%20every%20response%22&gs_l=serp.3...3951.5437.8.5971.7.7.0.0.0.1.107.526.6j1.7.0...0.0...1c.1.2.serp.pTydRwUG-uY&pbx=1&bav=on.2,or.r_gc.r_pw.r_cp.r_qf.&bvm=bv.42261806,d.d2k&fp=444189726e5cb09f&biw=1415&bih=825 [7]: https://www.google.co.uk/search?q=%22going%20for%20walking%22&btnG=Search%20Books&tbm=bks&tbo=1#hl=en&tbo=d&tbm=bks&sclient=psy-ab&q=%22whose%20each%20pair%22&oq=%22whose%20each%20pair%22&gs_l=serp.3...1550575.1552345.2.1552594.7.7.0.0.0.0.82.456.7.7.0...0.0...1c.1.2.serp.XFNDAWtmnn4&pbx=1&bav=on.2,or.r_gc.r_pw.r_cp.r_qf.&bvm=bv.42261806,d.d2k&fp=444189726e5cb09f&biw=1415&bih=825 [8]: https://www.google.co.uk/search?q=%22going%20for%20walking%22&btnG=Search%20Books&tbm=bks&tbo=1#hl=en&tbo=d&tbm=bks&sclient=psy-ab&q=%22whose%20each%20solution%22&oq=%22whose%20each%20solution%22&gs_l=serp.3...4207.8093.4.8364.7.7.0.0.0.0.84.448.7.7.0...0.0...1c.1.2.serp.VozHwO2NwlE&pbx=1&bav=on.2,or.r_gc.r_pw.r_cp.r_qf.&bvm=bv.42261806,d.d2k&fp=444189726e5cb09f&biw=1415&bih=825