The

ordered pair of neutrosophic duplets D = {(a - aI, 1 - dI); a [member of] [R.sup.+]; d [member of] R} forms a neutrosophic semigroup under product taken component wise.

These

ordered pairs indicate that a is mapped to y and a is mapped to z.

An

ordered pair ([bar.x],[bar.y]) is said to be an u x [epsilon]-optimal pair of ([P.sub.u]), if there exist [bar.x] [member of] X and [bar.y] [member of] F([bar.x]), such that

Digraph D consists of a finite set V of points (vertex) and a collection of

ordered pairs of distinct points.

Let Q = < ([o.sub.1], [q.sub.1]), ([o.sub.2], [q.sub.2),.....,([o.sub.n], [q.sub.n]) >, where element ([o.sub.i], [q.sub.i]) is composed of an

ordered pair o with time point q with Q representing mobile access arrangement in mobile with length n, namely for n-arrangement.

From this combined perspective, an

ordered pair of worlds would be closer to a given pair of worlds "the more each individual member of the pair resembles its corresponding member and the more the relations that hold between the members of the resembling pair resemble those that hold between the members of the original pair" (Garcia-Ramirez 2012, p.

(ii) The first element in the

ordered pairs of 1-hop list is the sensor itself.

We define S' by letting S' [intersection] O = S [intersection] O for every even-sized orbit O of [gamma], and S' [intersection] ([O.sub.1] [union] [O.sub.2]) = (S [intersection] ([O.sub.1] [union] [O.sub.2]))[degrees] for each

ordered pair ([O.sub.1]; [O.sub.2]) of odd-sized orbits of y from our fixed pairing of such orbits, as introduced above.

Written as

ordered pairs (x, y) according to Table 1, the coordinates of the stars are as follows: Atlas (66, 400); Alcyone (204, 468); Merope (224, 793); Maia (249, 336); Taygeta (488, 315); Electra (508, 858); and Celaeno (618, 640).

In linear algebra, an

ordered pair of numbers typically represents a vector, which in the present setting of coordinates can be taken to mean a change in location.

Two-place predicates can be phrased in the form "y is R-related to z," in which case an assignment is made between the predicate IS--R--RELATED--TO and the

ordered pair <y, z>.

All I will say is that an orthomodular lattice is a special sort of partially ordered set, where a partially ordered set is an

ordered pair <A, [less than or equal to] >, where A is a non-empty set and [less than or equal to] is a reflexive, transitive, antisymmetric relation defined on A.