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PIMSO 2025 - Mathematics - Senior Secondary - National Round Question 7

PIMSO Maths · PIMSO 2025 - Mathematics - Senior Secondary - National Round

Question 7

If $A=\{a_1,a_2,a_3,\ldots,a_m\}$, $B=\{b_1,b_2,b_3,\ldots,b_n\}$ and $C=\{c_1,c_2,c_3,\ldots,c_l\}$, then $A\times B\times C=\{a_1,a_2,a_3,\ldots,a_m\}\times\{b_1,b_2,b_3,\ldots,b_n\}\times\{c_1,c_2,c_3,\ldots,c_l\}$. Find the cardinality of the power set of $A\times B\times C$.
  1. $2^{mnl}$
  2. $2^{m+n+l}$
  3. $2^{mnl}-1$
  4. $m\times n\times l$