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GATE Mechanical 2023 | GA Question: 9

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By analyzing the question statement we have a set of $6$ elements each of these elements can have exactly $3$ possible states:

  1. Present in both the subsets $S$ and $T$
  2. Absent in both the subsets $S$ and $T$
  3. Present in $T$ but not present in $S$

Thus we get in total $3 \underbrace{\times} _{(6 \text{ times})} 3 = 3^6 = 729$ possibilities. 

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