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Help with two problems about relations
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For part (ii), you just need to go through the properties listed and verify if they're true (or provide a counterexample if not) for the two relations. It's quite simple if you understand what the relations do.

For part (i), this just looks like an exercise in understanding mathematical notation. They give you a way to write the numbers j and k in terms of the digits in their decimal representation. So can you find a way to write a mathematical statement about *those digits* that conveys what R1 and R2 are about? For R1, I'd write something like:

>j R1 k ⇔ { a\_m | j = Σ from {m = 0 to M} (a\_m ⋅ 10\^m) } ∩ { b\_n | k = Σ {from n = 0 to N (b\_n ⋅ 10\^n) } ≠ ∅

All that says is 'the decimal representations of j and k have at least one digit in common (not caring about order).' Can you think of a way to state R2?

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