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Let A and B be sets of vertices in a ( possibly infinite ) digraph G. Then there exists a family P of disjoint A-B-paths and a separating set which consists of exactly one vertex from each path in P.
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Let and B
Let exactly 1'' '' of `` A '' extend beyond `` B '' and use a square to check your angle to exactly 90 degrees.
Gloria Gaynor ( born September 7, 1949 ) is an American singer, best known for the disco era hits ; " I Will Survive " ( Hot 100 number 1, 1979 ), " Never Can Say Goodbye " ( Hot 100 number 9, 1974 ), " Let Me Know ( I Have a Right )" ( Hot 100 number 42, 1980 ) and " I Am What I Am " ( R & B number 82, 1983 ).
Let the input power to a device be a force F < sub > A </ sub > acting on a point that moves with velocity v < sub > A </ sub > and the output power be a force F < sub > B </ sub > acts on a point that moves with velocity v < sub > B </ sub >.
Let us take a hypothetical single scan line, with B representing a black pixel and W representing white:
Other chart hits by White included " Never, Never Gonna Give Ya Up " (# 2 R & B, # 7 Pop in 1973 ), " Can't Get Enough of Your Love, Babe " (# 1 Pop and R & B in 1974 ), " You're the First, the Last, My Everything " (# 1 R & B, # 2 Pop in 1974 ), " What Am I Gonna Do with You " (# 1 R & B, # 8 Pop in 1975 ), " Let the Music Play " (# 4 R & B in 1976 ), " It's Ecstasy When You Lay Down Next to Me " (# 1 R & B, # 4 Pop in 1977 ) and " Your Sweetness is My Weakness " (# 2 R & B in 1978 ).
Let M be the intersection of all subgroups of the free Burnside group B ( m, n ) which have finite index, then M is a normal subgroup of B ( m, n ) ( otherwise, there exists a subgroup g < sup >-1 </ sup > Mg with finite index containing elements not in M ).
Let and be
Let every policeman and park guard keep his eye on John and Jane Doe, lest one piece of bread be placed undetected and one bird survive.
Let us assume that it would be possible for an enemy to create an aerosol of the causative agent of epidemic typhus ( Rickettsia prowazwki ) over City A and that a large number of cases of typhus fever resulted therefrom.
Let p be the minimal polynomial for T, Af, where the Af, are distinct irreducible monic polynomials over F and the Af are positive integers.
Let V be a finite-dimensional vector space over an algebraically closed field F, e.g., the field of complex numbers.
Let N be a positive integer and let V be the space of all N times continuously differentiable functions F on the real line which satisfy the differential equation Af where Af are some fixed constants.
Let Q be a nonsingular quadric surface bearing reguli Af and Af, and let **zg be a Af curve of order K on Q.
Let us take a set of circumstances in which I happen to be interested on the legislative side and in which I think every one of us might naturally make such a statement.
Let the state of the stream leaving stage R be denoted by a vector Af and the operating variables of stage R by Af.
Let it be granted then that the theological differences in this area between Protestants and Roman Catholics appear to be irreconcilable.
Let us therefore put first things first, and make sure of preserving the human race at whatever the temporary price may be ''.
Let and sets
Using terms from formal language theory, the precise mathematical definition of this concept is as follows: Let S and T be two finite sets, called the source and target alphabets, respectively.
Let ρ be the initial topology on X induced by C < sub > τ </ sub >( X ) or, equivalently, the topology generated by the basis of cozero sets in ( X, τ ).
Let ( X, Σ ) and ( Y, Τ ) be measurable spaces, meaning that X and Y are sets equipped with respective sigma algebras Σ and Τ.
Let L < sub > 1 </ sub >, L < sub > 2 </ sub >, L ′< sub > 1 </ sub > and L ′< sub > 2 </ sub > be ordered sets.
In May 1966 they filmed two sets of colour promotional clips for their current single " Rain "/" Paperback Writer " all directed by Michael Lindsay-Hogg, who went on to direct The Rolling Stones Rock and Roll Circus and The Beatles final film Let It Be.
Let be the category of finite sets and bijections ( the collection of all finite sets, and invertible functions between them ).
Let S be a family of finite sets, where the family may contain an infinite number of sets and the individual sets may be repeated multiple times.
Let ( C, F ) be a concrete category ( i. e. F: C → Set is a faithful functor ), let X be a set ( called basis ), A ∈ C an object, and i: X → F ( A ) a map between sets ( called canonical injection ).
Let L / k be a finite extension of fields, and X a variety defined over L. The functor from k-schemes < sup > op </ sup > to sets is defined by
Let ( either the open or closed sets does not matter ) τ < sub > 1 </ sub > and τ < sub > 2 </ sub > be two topologies on a set X such that τ < sub > 1 </ sub > is contained in τ < sub > 2 </ sub >:
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