# Ace workbook lattice concept

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If X is minimum element of S then X is related to y for all y belongs to S. Let [S;R] be a poset. If every non empty subset of S has a minimum element then
a) S is Totally ordered set

b) S is bounded set.
C)  S is complemented lattice
d) S is boolean algebra.
Can anyone explain the exact meaning of question and what the answer would be?   Thanks in advance..
Ps:  what I understood from question is if X is minimum element then X will be part of every subset of S like if 1 is Min element in the set then 1 will be part of every non empty subset of S. Is this correct way of interpreting the question. If not can you please elaborate it

## Related questions

1
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Let $A=\left \{ 1,2,3 \right \}$. A relation $R$ on $A\times A$ is defined by $\left ( a,b \right )R\left ( c,d \right )\Leftrightarrow \left ( “a\leq c “and” b\leq d “\right )$ S1:$R$ partial order S2: The poset $\left [ A\times A:R \right ]$ is a lattice Among S1 and S2 which one is true?