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Question Number 169664 by MathsFan last updated on 05/May/22

Given that n(A)=10 and n(B)=6 i) what is the largest possible of n(A∪B) ii) what is the smallest possible value of n(A∪B) iii) what is the smallest possible value of n(A∩B)

$$\:\boldsymbol{\mathrm{Given}}\:\boldsymbol{\mathrm{that}}\:\boldsymbol{\mathrm{n}}\left(\boldsymbol{\mathrm{A}}\right)=\mathrm{10}\:\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{n}}\left(\boldsymbol{\mathrm{B}}\right)=\mathrm{6} \\ $$$$\left.\:\boldsymbol{\mathrm{i}}\right)\:\boldsymbol{\mathrm{what}}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{largest}}\:\boldsymbol{\mathrm{possible}}\:\boldsymbol{\mathrm{of}}\: \\ $$$$\:\:\:\:\:\:\boldsymbol{\mathrm{n}}\left(\boldsymbol{\mathrm{A}}\cup\boldsymbol{\mathrm{B}}\right) \\ $$$$\left.\:\boldsymbol{\mathrm{ii}}\right)\:\boldsymbol{\mathrm{what}}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{smallest}}\:\boldsymbol{\mathrm{possible}}\:\boldsymbol{\mathrm{value}} \\ $$$$\:\:\:\:\:\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{n}}\left(\boldsymbol{\mathrm{A}}\cup\boldsymbol{\mathrm{B}}\right) \\ $$$$\left.\boldsymbol{\mathrm{iii}}\right)\:\boldsymbol{\mathrm{what}}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{smallest}}\:\boldsymbol{\mathrm{possible}}\:\boldsymbol{\mathrm{value}} \\ $$$$\:\:\:\:\:\:\:\boldsymbol{\mathrm{of}}\:\:\boldsymbol{\mathrm{n}}\left(\boldsymbol{\mathrm{A}}\cap\boldsymbol{\mathrm{B}}\right) \\ $$$$ \\ $$

Answered by Rasheed.Sindhi last updated on 05/May/22

(i) The largest possible of n(A∪B)=n(A)+n(B)=10+6=16 (ii)The smallest possible value of n(A∪B)=max( n(A),n(B) )=10 (iii)The smallest possible value of n(A∩B)=0

$$\left({i}\right)\:\mathcal{T}{he}\:{largest}\:{possible}\:{of} \\ $$$$\:\:\:{n}\left({A}\cup{B}\right)={n}\left({A}\right)+{n}\left({B}\right)=\mathrm{10}+\mathrm{6}=\mathrm{16} \\ $$$$\left({ii}\right)\mathcal{T}{he}\:{smallest}\:{possible}\:{value}\:{of} \\ $$$$\:\:{n}\left({A}\cup{B}\right)={max}\left(\:{n}\left({A}\right),{n}\left({B}\right)\:\right)=\mathrm{10} \\ $$$$\left({iii}\right)\mathcal{T}{he}\:{smallest}\:{possible}\:{value}\:{of} \\ $$$$\:\:{n}\left({A}\cap{B}\right)=\mathrm{0} \\ $$

Commented by MathsFan last updated on 05/May/22

Thank you sir i appreciate sir

$${Thank}\:{you}\:{sir} \\ $$$$\:{i}\:{appreciate}\:{sir} \\ $$

Commented by peter frank last updated on 06/May/22

thank you

$$\mathrm{thank}\:\mathrm{you} \\ $$

Commented by Rasheed.Sindhi last updated on 06/May/22

thank you FOR ′thank you′!

$$\mathrm{thank}\:\mathrm{you}\:\mathrm{FOR}\:'\mathrm{thank}\:\mathrm{you}'! \\ $$

Commented by MathsFan last updated on 10/May/22

😇

$$ \\ $$😇

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