Let R be a quasi-ordering and let S be the relation on the set of equivalence classes of R ∩ R − 1 such that ( C , D ) belongs to 5, where C and D are equivalence classes of R , if and only if there are elements c of C and d of D such that ( c, d ) belongs to R . Show that S is a partial ordering. Let L be a lattice. Define the meet ( ∧ ) and join ( ∨ ) operations by x ∧ y = glb ( x , y ) and x ∨ y = lub ( x , y ) .
Let R be a quasi-ordering and let S be the relation on the set of equivalence classes of R ∩ R − 1 such that ( C , D ) belongs to 5, where C and D are equivalence classes of R , if and only if there are elements c of C and d of D such that ( c, d ) belongs to R . Show that S is a partial ordering. Let L be a lattice. Define the meet ( ∧ ) and join ( ∨ ) operations by x ∧ y = glb ( x , y ) and x ∨ y = lub ( x , y ) .
Solution Summary: The author explains that R is a quasi-ordering and S be the relation on the set of equivalence classes of
LetRbe a quasi-ordering and let S be the relation on the set of equivalence classes of
R
∩
R
−
1
such that (C,D) belongs to 5, whereCandDare equivalence classes ofR, if and only if there are elementscofCanddofDsuch that (c, d) belongs toR. Show thatSis a partial ordering.
LetLbe a lattice. Define the meet
(
∧
)
and join
(
∨
)
operations by
x
∧
y
=
glb
(
x
,
y
)
and
x
∨
y
=
lub
(
x
,
y
)
.
The diagram below models the layout at a carnival where G, R, P, C, B, and E are various locations on the grounds. GRPC is a parallelogram.
19
G
R
375 ft
425 ft
325 ft
B 225 ft
P
E
Part A: Identify a pair of similar triangles. (2 points)
Part B: Explain how you know the triangles from Part A are similar. (4 points)
Part C: Find the distance from B to E and from P to E. Show your work. (4 points)
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RELATIONS-DOMAIN, RANGE AND CO-DOMAIN (RELATIONS AND FUNCTIONS CBSE/ ISC MATHS); Author: Neha Agrawal Mathematically Inclined;https://www.youtube.com/watch?v=u4IQh46VoU4;License: Standard YouTube License, CC-BY