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Q.
If $aN = {ax : x \in N}$ and $bN \cap cN = dN$, where $b,\, c \in N$ are relatively prime, then
Sets
Solution:
bN = {$bx : x \in N$}
cN = {$cx : x \in N$}
$\therefore bN \cap cN =$ {x : x is multiple of b and c both}
$=$ { x: x is multiple of l.c.m. of b and c }
$=$ { x : x is multiple of b c}
[given b and c are relatively prime $\therefore $ l.c.m. of b and $c = bc$]
$\therefore bN \cap cN = {bc x : x \in N} = dN$ (Given)
$\therefore d = bc.$