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A quick definition clarification: Does the set $\{(x,y):x =0 \,\,\,\,\text{or} \,\,\,\,y=1 \}$ include the element $(0,1)$? (Sorry, English is not my first language, I get confused sometimes... Also sorry that this may not be a very good math question.) Thanks.

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Yes. A or B means that A is true and B is false, or B is true and A is false, or that both are true.

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Thanks, Florian! – defor Nov 9 '11 at 11:25
'Or' as in 'sugar or milk?' rather than 'tea or coffee?' :) – tom Nov 9 '11 at 11:26
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@defor The usage of OR as in this answer (and also in "sugar or milk?") is commonly called an inclusive or. In contrast, the one in "tea or coffee?" is an exclusive or. In mathematical writing, we conventionally use inclusive or's unless otherwise mentioned. – Srivatsan Nov 9 '11 at 11:52

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