Question Solved1 Answer 4. Is (S, R) a poset if S is the set of all people in the world and (a, b) E R, where a and b are people, if a) a is no shorter than b? b) a weighs more than b? c) a = b or a is a descendant of b? d) a and b do not have a common friend?

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Transcribed Image Text: 4. Is (S, R) a poset if S is the set of all people in the world and (a, b) E R, where a and b are people, if a) a is no shorter than b? b) a weighs more than b? c) a = b or a is a descendant of b? d) a and b do not have a common friend?
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Transcribed Image Text: 4. Is (S, R) a poset if S is the set of all people in the world and (a, b) E R, where a and b are people, if a) a is no shorter than b? b) a weighs more than b? c) a = b or a is a descendant of b? d) a and b do not have a common friend?
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Posets A partially ordered set (normally, poset) is a set, L, together with a relation, u2264, that obeys, for all a, b, c u2208 L: (reflexivity) a u2264 a; (anti-symmetry) if a u2264 b and b u2264 a then a = b; and (transitivity) if a u2264 b and b u2264 c then a u2264 c. The relation u2264 is called a partial order on LSldions since to know that a relation R on set A If is sard to be posel (panhal ordes set)(1) R is reflexiveie AA a in A=>(a,a)in RR is antisymmetricie AA a,b in Aif (a,b)in R and (b,a)in R=>a=b(3) R is fransitivele AA a,b,c in Ast (a,b)in R,(b,c)in R=>(a,c)in RNow here it is given thatS={n:x is a peaple in the world }(a) R={(a,b):a is no shorten than b,a,b in S}=>R=(a,b):a >= b}i. (a,b)inR tow heighto of a >= height of b.Br as reflexive :' hight of a= height a.But R is not antisymmeticbeculs ... See the full answer