Question Number 4733 by Yozzii last updated on 02/Mar/16 Commented by Yozzii last updated on 02/Mar/16 $${How}\:{can}\:{you}\:{show}\:{that}\: \\ $$$$\left(\cup{S}\right)×\left(\cup{T}\right)\nsupseteq\cup\left\{{X}×{Y}\:\mid{X}\in{S},{Y}\in{T}\right\}? \\ $$ Commented by prakash jain…
Question Number 135634 by oustmuchiya@gmail.com last updated on 14/Mar/21 Answered by physicstutes last updated on 14/Mar/21 $$\left({i}\right)\:{n}\left({B}\right)\:=\:\mathrm{8}\:+\:\mathrm{5}\:+\:{x}−\mathrm{4}\:=\:\mathrm{11}\:+\:{x} \\ $$$$\:{n}\left(\:{B}\cup{C}\right)\:=\:\mathrm{8}+\:{x}−\mathrm{4}\:+\:\mathrm{5}\:+\:\mathrm{2}{y}\:=\:\mathrm{9}\:+\:{x}\:+\:\mathrm{2}{y} \\ $$$$\Rightarrow\:\:\mathrm{11}\:+\:{x}\:=\:\mathrm{9}\:+{x}\:+\:\mathrm{2}{y}\:\:\Rightarrow\:\:\:\mathrm{2}\:=\:\mathrm{2}{y}\:\Rightarrow\:{y}\:=\:\mathrm{1} \\ $$$$\left({ii}\right)\:{n}\left({C}\right)\:=\:\mathrm{5}\:+\:\mathrm{2}{y}\: \\ $$$$\mathrm{and}\:{n}\left({A}\right)\:=\:\mathrm{15}…
Question Number 69568 by Ajao yinka last updated on 25/Sep/19 Commented by mathmax by abdo last updated on 25/Sep/19 $$\:{if}\:{n}=\mathrm{1}\:\:\:\:\:\:{H}\:={C}\:\:\:\:\:{if}\:{n}\neq\mathrm{1}\:\:{we}\:{have}\:{z}={z}^{{n}} \:\Leftrightarrow\:{z}^{{n}−\mathrm{1}} =\mathrm{1}\:\:\:{let}\:{z}\:={r}\:{e}^{{i}\theta} \:\:{so} \\ $$$${z}^{{n}−\mathrm{1}}…
Question Number 4027 by Rasheed Soomro last updated on 27/Dec/15 $${Let}\:\mathbb{A}\:{denotes}\:{the}\:{Set}\:{of}\:{Algebraic}\:{Numbers} \\ $$$${and}\:\:\mathbb{T}\:\:\:{the}\:{Set}\:{of}\:{Trancedental}\:{Numbers}. \\ $$$${Discuss}\:{the}\:{following}: \\ $$$$\bullet{Are}\:\mathbb{A}\:{and}\:\mathbb{T}\:\:\boldsymbol{{closed}}\:{with}\:{respect}\:{to}\:\: \\ $$$$\boldsymbol{{addition}}\:{and}\:\boldsymbol{{multiplication}}\:? \\ $$$$\bullet{Are}\:\mathbb{A}−\left\{\mathrm{0}\right)\:\:{and}\:\mathbb{T}\:\:\boldsymbol{{closed}}\:{with}\:{respect}\:{to}\:\: \\ $$$$\boldsymbol{{division}}? \\ $$…
Question Number 3551 by prakash jain last updated on 15/Dec/15 $$\mathrm{Prove}\:\mathrm{that}\:\mathbb{P}\:\mathrm{set}\:\mathrm{of}\:\mathrm{prime}\:\mathrm{numbers}\:\mathrm{is} \\ $$$$\mathrm{countable}. \\ $$ Commented by Filup last updated on 15/Dec/15 $$\mathrm{ah},\:\mathrm{i}\:\mathrm{understand}\:\mathrm{the}\:\mathrm{question}\:\mathrm{now}. \\ $$$$\mathrm{I}\:\mathrm{can}'\mathrm{t}\:\mathrm{answer}\:\mathrm{it},\:\mathrm{though}…
Question Number 3130 by Rasheed Soomro last updated on 05/Dec/15 $${If}\:{A},{B},{C}\:{and}\:{D}\:{are}\:{any}\:{four}\:{sets}\:{then} \\ $$$$\left({i}\right)\:\:\left({A}−{B}\right)\cup\left({C}−{D}\right)\overset{?} {=}\left({A}\cup{C}\right)−\left({B}\cup{D}\right) \\ $$$$\left({ii}\right)\:\left({A}−{B}\right)\cup\left({C}−{D}\right)\overset{?} {=}\left({A}\cup{C}\right)−\left({B}\cap{D}\right) \\ $$ Answered by prakash jain last updated…
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Question Number 133419 by liberty last updated on 22/Feb/21 $$\mathrm{Prove}\:\mathrm{the}\:\mathrm{set}\:\left\{\mathrm{1},\mathrm{2},\mathrm{3},…,\mathrm{1989}\right\} \\ $$$$\mathrm{can}\:\mathrm{be}\:\mathrm{expressed}\:\mathrm{as}\:\mathrm{the}\:\mathrm{disjoint} \\ $$$$\mathrm{union}\:\mathrm{of}\:\mathrm{A}_{\mathrm{1}} ,\mathrm{A}_{\mathrm{2}} ,…,\mathrm{A}_{\mathrm{117}} \:\mathrm{such}\:\mathrm{that} \\ $$$$\left(\mathrm{i}\right)\:\mathrm{each}\:\mathrm{A}_{\mathrm{i}} \:\mathrm{contains}\:\mathrm{the}\:\mathrm{same}\:\mathrm{number}\:\mathrm{of}\:\mathrm{elements}\:,\mathrm{and} \\ $$$$\left(\mathrm{ii}\right)\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{all}\:\mathrm{elements}\:\mathrm{of}\:\mathrm{each}\:\mathrm{A}_{\mathrm{i}} \:\mathrm{is} \\ $$$$\mathrm{the}\:\mathrm{same}\:\mathrm{for}\:\mathrm{i}=\mathrm{1},\mathrm{2},\mathrm{3},…,\mathrm{m}…
Question Number 1875 by Filup last updated on 20/Oct/15 $$\mathrm{Given}\:\mathrm{that}: \\ $$$${Z}=\left\{\mathrm{0},\:\mathrm{1},\:\mathrm{2},\:…\right\}\:\mathrm{all}\:\mathrm{integers}\:\geqslant\mathrm{0} \\ $$$${R}=\left\{\mathrm{0},\:\mathrm{0}.\mathrm{01},\:…,\:\mathrm{1},\:\mathrm{1}.\mathrm{01},\:…\right\}\:\mathrm{all}\:\mathrm{reals}\:\geqslant\mathrm{0} \\ $$$$\:\mathrm{Prove}\:\mathrm{that}\:\mid{R}\mid>\mid{Z}\mid \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 1763 by Gerlândio Almeida last updated on 18/Sep/15 $$ \\ $$ Commented by 123456 last updated on 18/Sep/15 $${p}_{\mathrm{0}} \left({n}\right)={xn} \\ $$$${r}\left({n}\right)=\alpha{xn} \\…