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-

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

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

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