Question

Needed full explanation of question 8.​

Answer 1

★ Answer

→ Refer to the attachment

Answer 2

$\huge\boxed{\underline{\mathcal{\red{A}\green{N}\pink{S}\orange{W}\blue{E}\pink{R}}}}$

${\bf{\green{let}}}$${\bf{\green{'x' }}}$${\bf{\green{be}}}$${\bf{\green{the}}}$${\bf{\green{set}}}$${\bf{\green{of}}}$${\bf{\green{people }}}$${\bf{\green{in}}}$${\bf{\green{the}}}$${\bf{\green{committe}}}$${\bf{\green{who}}}$${\bf{\green{speak}}}$${\bf{\green{French,}}}$${\bf{\orange{and}}}$${\bf{\pink{'Y' }}}$${\bf{\pink{be}}}$${\bf{\pink{the}}}$${\bf{\pink{set}}}$${\bf{\pink{of}}}$${\bf{\pink{people }}}$${\bf{\pink{in}}}$${\bf{\pink{the}}}$${\bf{\pink{committe}}}$${\bf{\pink{who}}}$${\bf{\pink{speak }}}$${\bf{\pink{Spanish}}}$

${\bf{\blue{NO. }}}$${\bf{\blue{of}}}$${\bf{\blue{people }}}$${\bf{\blue{who}}}$${\bf{\blue{speak }}}$${\bf{\blue{French }}}$${\bf{\blue{=n(X) }}}$${\bf{\blue{=50}}}$

${\bf{\red{NO.}}}$${\bf{\red{of }}}$${\bf{\red{people }}}$${\bf{\red{who }}}$${\bf{\red{speak }}}$${\bf{\red{Spanish }}}$${\bf{\red{=n(Y) }}}$${\bf{\red{=20}}}$

${\bf{\green{NO. }}}$${\bf{\green{of}}}$${\bf{\green{people }}}$${\bf{\green{who }}}$${\bf{\green{speak }}}$${\bf{\green{both }}}$${\bf{\red{French }}}$${\bf{\green{and}}}$${\bf{\pink{Spanish}}}$${\bf{\green{=n(X∩Y) }}}$${\bf{\green{=10}}}$

${\bf{\orange{people }}}$${\bf{\orange{who}}}$${\bf{\orange{speak }}}$${\bf{\orange {at least }}}$${\bf{\orange {one}}}$${\bf{\orange{language }}}$${\bf{\orange{=n(XUY) }}}$${\bf{\blue{=? }}}$

WKT,

${\bf{\green{n(XUY)=}}}$${\bf{\pink{n(X) +n(Y) }}}$${\bf{\blue{-n(X∩Y) }}}$

${\bf{\red{=>n(XUY) =50+20-10}}}$

${\bf{\blue{=>n(XUY)=70-10}}}$

${\bf{\pink{=>n(XUY)=60}}}$

${\bf{\green{therefore, }}}$${\bf{\orange{in the}}}$${\bf{\blue{committe}}}$${\bf{\red{speak }}}$${\bf{\green{at least }}}$${\bf{\pink{one}}}$${\bf{\blue{of }}}$ ${\bf{\green{two }}}$${\bf{\red{languages}}}$${\bf{\blue{=60}}}$