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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?

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