Let L be a lattice. Then prove that a Ù b=a if and only if a v b=b.
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Let be a lattice. We want to prove that if and only if
Suppose , since . Thus,
if , since , thus is a upper bound of and , by definition of least upper bound we have . since is an upper bound of and , , so
Suppose , since . Thus,
if , since , thus is a upper bound of and , by definition of least upper bound we have . since is an upper bound of and , , so