Interpreting "pairwise"

Question

I have the following exercise.

Can four lines in space (not necessarily passing through the same point) be pairwise perpendicular?

Does it mean (given 4 lines $a$, $b$, $c$, and $d$):

or

$a\perp b$, $a\perp c$, and $a\perp d$; $b\perp c$ and $b\perp d$; and $c\perp d$

?

How is "pairwise" to be interpreted?

NOTE: I do NOT need help solving the exercise.

score 2 · Accepted Answer · answered Sep 22 '16 at 04:29

2

It means that all pairs of lines are perpendicular.

Skipping redundant pairs

a is perpendicular to b.

a is perpendicular to c.

a is perpendicular to d.

b is perpendicular to c.

b is perpendicular to d.

c is perpendicular to d.

answered Sep 22 '16 at 04:29

Q the Platypus

Graham Kemp · Answer 2 · 2016-09-22T04:46:57.697

1

Pairwise (something): any/every pair from the set are (something).

The question is asking: Can you have a set of four lines such that if you select any/every pair of them they are perpendicular?

Or does $\{(a,b,c,d): a\perp b, a\perp c, a\perp d, b\perp c, b\perp d, c\perp d\}=\varnothing$ ? (empty set. ie: Is it that there are no such set?)

edited Sep 22 '16 at 04:46

answered Sep 22 '16 at 04:31

Graham Kemp

Thanks! A side question: what does the Ø mean? – Fine Man Sep 22 '16 at 04:38
1

Empty set. Or in this case it means "There is no possible examples of this". – Q the Platypus Sep 22 '16 at 04:44