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In colloquial English AND is often misused, or at least misunderstood, as meaning OR, and vice versa.

Thus, when writing a webpage instructing people to enter locations and distances from those locations to determine a search area by the INTERSECTION of those circles rather than their union, how might I express the instruction both clearly and simply?

I've currently got:

enter image description here

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    That is how you do it. Also, this strikes me as something that ux.stackexchange.com would be able to answer. – SomethingDark Oct 5 '16 at 21:35
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    You could also put 'both' after 'are', omitting 'also', for two constraints. – Edwin Ashworth Oct 5 '16 at 21:40
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    One work-around that I have seen to avoid this issue is to provide a separate form element allowing the users to choose between "search for all conditions" and "search for any condition". – Mick Oct 5 '16 at 21:40
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    I'm voting to close this question as off-topic because it is a well-studied problem in user interface design, and can be better answered elsewhere. – jimm101 Oct 5 '16 at 21:44
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    @jimm101: please provide a link? – Ian Oct 5 '16 at 21:45
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The "also" in your form is redundant. "AND" is sufficient. It is not accepted usage to interpret it as anything but a combination of the two, which does not allow for only one of them to satisfy the conditions.

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    I agree totally that AND should be sufficient/"also" is redundant. Regrettably though, in colloquial usage, it seems that is not. Hence my search for a plain and simple version instruction unambiguously interpretable. – Ian Oct 5 '16 at 22:00
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    We have an expression in AmE that you may be familiar with: "You can't fix stupid." If the form conforms with normal usage as it is taught, then you may find that varying from that a) causes confusion, b) discredits the form (and possibly the whole site) by making the form creator appear to have poor mastery of the language, c) doesn't solve the problem because visual cues are misleading. One alternative solution might be to place the fields adjacent to each other, rather than in separate visual zones vertically. This implies they have equal importance; upper-lower implies superiority. – jaxter Oct 5 '16 at 23:21
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From @FumbleFingers:

"It seems to me the obvious way to disambiguate is simply to reinstate one "deleted" word from

Find places that are [condition #1] and are also [condition #2].

This explicitly forces also to apply to both instances of are, ruling out the possibility of it applying to and also find (which alternative gives rise to the or interpretation)."

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Although 'and' alone expresses the intended conjunctive meaning, it is as you mention liable to misinterpretation. To head that misinterpretation off at the pass, so to speak, you can use "the modern colourless" 'while'. This use of while has the additional advantage (if you like) of applying to mobile 'places'. For example, 'while' applies both conditions to airplanes, helicopters, automobiles, RVs (caravans), mobile homes or offices, but only while such 'places' are within 200 miles of both Birmingham and London.

while, ... conj. ...
....
c. In modern colourless use: At the same time that, besides that, in addition to the fact that; often = and at the same time, and besides.

["while, adv. (and adj.) and conj. (and prep.)". OED Online. September 2016. Oxford University Press. http://www.oed.com/view/Entry/228336?rskey=wQr12H&result=3&isAdvanced=false (accessed October 07, 2016).]

As indicated by extrapolation from that definition, 'and at the same time' or, more likely, 'and besides' would also suit your purposes. I find such constructions less graceful than the simple 'while also', but 'and besides' might better suit your sense of the colloquial.

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