in a group of 40 students,26 take samosa,18 take burgers,and 8 takes neither of the two amd who takes both?

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$$\begin{gathered} \mathrm{Samosa}\to \mathrm{S} \\ \mathrm{Burgers}\to \mathrm{B} \\ \mathrm{Now} \mathrm{as} 8 \mathrm{students} \mathrm{take} \mathrm{neither} \mathrm{of} 2, \mathrm{hence} \mathrm{number} \mathrm{of} \mathrm{students} \mathrm{who} \mathrm{like} \\ \mathrm{either} \mathrm{S} \mathrm{or} \mathrm{B} \mathrm{are} \mathrm{given} \mathrm{by} \\ \mathrm{n}\left(\mathrm{S}\cup \mathrm{B}\right)=40-8=32 \\ \mathrm{According} \mathrm{to} \mathrm{ques} \\ \mathrm{n}\left(\mathrm{S}\right)=26 \\ \mathrm{n}\left(\mathrm{B}\right)=18 \\ \mathrm{We} \mathrm{know} \mathrm{that} \\ \mathrm{n}\left(\mathrm{S}\cup \mathrm{B}\right)=\mathrm{n}\left(\mathrm{S}\right)+\mathrm{n}\left(\mathrm{B}\right)-\mathrm{n}\left(\mathrm{S}\cap \mathrm{B}\right) \\ \Rightarrow 32=26+18-\mathrm{n}\left(\mathrm{S}\cap \mathrm{B}\right) \\ \Rightarrow \mathrm{n}\left(\mathrm{S}\cup \mathrm{B}\right)=44-32 \\ \Rightarrow \mathrm{n}\left(\mathrm{S}\cap \mathrm{B}\right)=12 \\ \mathrm{Hence} 12 \mathrm{students} \mathrm{take} \mathrm{both}. \end{gathered}$$

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