Need help with A-F OF SE, ESign In or Sign Upl Chegg. \' O u clackboard.com/bb s

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Need help with A-F

OF SE, ESign In or Sign Upl Chegg. ' O u clackboard.com/bb s webdav/pid-5571887 dt content--576 8112 corses/2017 fall cs 151.34 58/cs%201 51%2%20 ewm b. If both f and g are surjective (onto), then f og is also surjective. Explain why. Part IlII: Relations (50 pt.) 1. (30 pt., 5 pt. each) For each of the following relations, determine whether the relation is: Reflexive. Anti-reflexive. Symmetric. Anti-symmetric Transitive A partial order. A strict order. .A total order. An equivalence relation. Justify your answers a, R is a relation on the set { 1, 2, 34) such that R = {(1,1), (1,2), (2,1), (2,2), (3,3), (4,4). b. R is a relation on the set of all people such that (a, b) E R if and only if a and b have a common grandparent. c. R is a relation on the power set of a set A such that (x, y) E R if and only if x c y. d. R is a relation on Z+ such that (x,y) e R if and only if x divides y. e, R is a relation on Z such that (x,y) E R if and only if y f. R is a relation on Z such that (x. y) e R if and only if xy 2 1. Type here to search

Explanation / Answer

a)

Reflexive : contains {(1,1),(2,2),(3,3),(4,4)}

Symmetric : contains {(1,2),(2,1)}

Transitive : contains {(1,2),(2,1),(1,1)}

Equivalence: Because its reflexive, symmetric & transitive

b)

Reflexive : Grandparent of itself would be same

Symmetric : If grandparent of a & b is same then grandparent of b & a will also be same

Transitive : If grandparent of a & b is same and grandparent of b & c is same then grandparent of a & c will also be same

Equivalence: Because its reflexive, symmetric & transitive

c)

Anti-refleive : A set is subset of itself but is not proper subset of itself, here proper subset is used.

Anti-symmetric : If x y then y x is false.

Transitive: If x y & y z then x z

d)

Reflexive : Every integer divides itself

Anti-symmetric: If x divides y then y divides x is false

Transitive: If x divides y & y divides z then z divides z.

Partial Order: Because its reflexive, anti-symmetric & transitive

e)

Anti-reflexive : R contains integers such that x y. For relation to be reflexive x = y

Symmetric: If x y then y x is true

f)

Anti-relfexive : For 0 Z, (0,0) does not belong to relation since 0x0 < 1

Symmetric : If xy >= 1 then yx>=1

Transitive : If xy>=1 & yz>=1 then xz >=1. [for xy >= either both are positive or both are negative, so if y is positive then both x & z has to be positive to make multiplication >=1 or if y is negative then both have to be negative In either case either both x & z are positive or both are negative and their product will always be >=1. Thus (x,z) will also belong to relation]

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