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Question: Answered & Verified by Expert
If A. B and $\mathrm{C}$ are any three arbitraryevents then which one of the following expressions shows that both $\mathrm{A}$ and $\mathrm{B}$ occur but not C ?
MathematicsSets and RelationsNDANDA 2006 (Phase 1)
Options:
  • A $\mathrm{A} \cap \overline{\mathrm{B}} \cap \overline{\mathrm{C}}$
  • B $\mathrm{A} \cap \mathrm{B} \cap \overline{\mathrm{C}}$
  • C $\overline{\mathrm{A}} \cap \overline{\mathrm{B}} \cap \overline{\mathrm{C}}$
  • D $(\mathrm{A} \cup \mathrm{B}) \cap \overline{\mathrm{C}}$
Solution:
2221 Upvotes Verified Answer
The correct answer is: $\mathrm{A} \cap \mathrm{B} \cap \overline{\mathrm{C}}$
If A, B and C are any three arbitrary events occurrence of both A and B is given by A $\cap$ Band non-occurrence
of $\mathrm{C} a s \overline{\mathrm{C}}$ then the event both $\mathrm{A}$ and $\mathrm{B}$ occur but not $\mathrm{C}$
is represented by $\mathrm{A} \cap \mathrm{B} \cap \overline{\mathrm{C}}$.

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