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asked in Set Theory & Algebra by Boss (6.5k points) 19 134 236
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(1)Upper bound of S= { 3 , 4 , 5 , 6 , 7 , 8 }

Lower bound of S=not Exists

Upper bound of S= { 6 , 7 , 8 }

Lower bound of S= { 1, 2, 3 }

 

(2)GLB(S1)=not Exists

LUB(S1)=not Exists

 

GLB(S2)= 3

LUB(S2)=not Exists

answered by Veteran (35.3k points) 11 49 233
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LUB(S1) is  3 ??

LUB(S2) is 3 ??
no both are wrong.
Reason plz
do you know what is LUB?
Not..actually... If u explain ..it will be beneficial to me..

make arrow in image 

for LUB = go for upward direction from that set and take 1st meeting point .

for GLB = go for lower direction from that set and take 1st meeting point .

 

@Anirudh. Plz guide me.

LUB(S1)=3     I think because this is the first meeting pt of 1 and 2, right?

LUB(S2)=6    I think because 3,4,5 meet here for the first time, right?

everything is fine but Lub of  s1 should be 3 as you considered the set of all upperbound of s1 here {3,4,5,6,7,8} then least upper bound of s1 should be 3
Why there is 3 in lower bound of S2={3,4,5}
LUB for S1 is 3 and LUB for S2 is 8 or not exist ?


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