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Draw an Appropriate Venn Diagram and Use the Given Information

question 146

Multiple Choice

Draw an appropriate Venn diagram and use the given information to fill in the number of elements in each region.
- n(A) =35,n(AB) =24,n(AC) =15,n(BC) =14,n(ABC) =10,n(ABC) =6\mathrm { n } ( \mathrm { A } ) = 35 , \mathrm { n } \left( \mathrm { A } \cap \mathrm { B } ^ { \prime } \right) = 24 , \mathrm { n } ( \mathrm { A } \cap \mathrm { C } ) = 15 , \mathrm { n } ( \mathrm { B } \cap \mathrm { C } ) = 14 , \mathrm { n } \left( \mathrm { A } ^ { \prime } \cap \mathrm { B } ^ { \prime } \cap \mathrm { C } ^ { \prime } \right) = 10 , \mathrm { n } ( \mathrm { A } \cap \mathrm { B } \cap \mathrm { C } ) = 6 \text {, }
n(BC) =52,n(BC) =18\mathrm { n } ( \mathrm { B } \cup \mathrm { C } ) = 52 , \mathrm { n } \left( \mathrm { B } \cap \mathrm { C } ^ { \prime } \right) = 18

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Definitions:

Off-Resonance Decoupled

A technique in NMR spectroscopy used to simplify the spectrum by selectively removing couplings between nuclei.

Proton Spin Decoupled

A nuclear magnetic resonance (NMR) technique used to simplify spectra by removing proton-proton coupling interactions.

Down Field

In NMR spectroscopy, referring to shifts in resonance frequency towards lower magnetic field strengths, often indicating an electron-withdrawing environment.

Proton Spin Decoupled

A technique in NMR spectroscopy where the interactions between proton spins are removed or decoupled, simplifying the spectrum and making it easier to interpret.

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