Parad Gandhak Bhasm (Mercury-Sulfur Ash) in Ayurveda

 

Problem:

Let $L$ be a lattice with the elements $a, b, c$, where the meet ($\wedge$) and join ($\vee$) operations satisfy the following conditions:

1. $a \vee b = b$
2. $a \wedge c = a$
3. $b \wedge c = c$

Questions:

1. Show that $a \leq b$ in the lattice order.
2. Show that $c \leq b$ in the lattice order.
3. Can you determine the greatest and least elements of this lattice, if they exist?

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Hints:

• Recall that in a lattice, $x \leq y$ if and only if $x \vee y = y$ (or equivalently $x \wedge y = x$).
• Use the given conditions to derive relations between elements.