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Category: Set Theory

In-an-exam-36-of-people-failed-in-physics-and-49-failed-in-maths-and-15-failed-in-both-subject-If-the-total-number-of-student-that-passed-physics-only-is-680-find-the-total-number-of-students-t

Question Number 122426 by Lordose last updated on 16/Nov/20 $$ \\ $$$$\mathrm{In}\:\mathrm{an}\:\mathrm{exam}\:\mathrm{36\%}\:\mathrm{of}\:\mathrm{people}\:\mathrm{failed}\:\mathrm{in}\: \\ $$$$\mathrm{physics}\:\mathrm{and}\:\mathrm{49\%}\:\mathrm{failed}\:\mathrm{in}\:\mathrm{maths}\:\mathrm{and}\:\mathrm{15\%} \\ $$$$\mathrm{failed}\:\mathrm{in}\:\mathrm{both}\:\mathrm{subject}.\:\mathrm{If}\:\mathrm{the}\:\mathrm{total}\: \\ $$$$\mathrm{number}\:\mathrm{of}\:\mathrm{student}\:\mathrm{that}\:\mathrm{passed}\:\mathrm{physics} \\ $$$$\mathrm{only}\:\mathrm{is}\:\mathrm{680}\:\mathrm{find}\:\mathrm{the}\:\mathrm{total}\:\mathrm{number}\:\mathrm{of} \\ $$$$\mathrm{students}\:\mathrm{that}\:\mathrm{appeared}\:\mathrm{in}\:\mathrm{the}\:\mathrm{exam}\:. \\ $$ Terms…

If-R-be-a-relation-on-a-set-of-real-number-defined-by-R-x-y-x-2-y-2-0-find-i-R-in-roster-form-ii-Domain-of-R-iii-Range-of-R-

Question Number 56744 by Umar last updated on 22/Mar/19 $$\mathrm{If}\:\mathrm{R}\:\mathrm{be}\:\mathrm{a}\:\mathrm{relation}\:\mathrm{on}\:\mathrm{a}\:\mathrm{set}\:\mathrm{of}\:\mathrm{real}\:\mathrm{number} \\ $$$$\mathrm{defined}\:\mathrm{by}\:\mathrm{R}=\left\{\left(\mathrm{x},\mathrm{y}\right):\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} =\mathrm{0}\right\}, \\ $$$$\mathrm{find}\: \\ $$$$\:\:\mathrm{i}−\:\mathrm{R}\:\mathrm{in}\:\mathrm{roster}\:\mathrm{form} \\ $$$$\:\:\mathrm{ii}−\mathrm{Domain}\:\mathrm{of}\:\mathrm{R} \\ $$$$\:\:\mathrm{iii}−\mathrm{Range}\:\mathrm{of}\:\mathrm{R}\: \\ $$ Answered…

number-theory-m-n-N-m-n-1-prove-m-n-n-m-mn-1-n-x-N-x-lt-n-x-n-1-m-n-

Question Number 121870 by mnjuly1970 last updated on 12/Nov/20 $$\:\:\:\:\:\:{number}\:\:{theory}: \\ $$$$\:\:\:\:\:\:{m},{n}\:\in\:\mathbb{N}\:\:,\:\:\left({m},{n}\right)=\mathrm{1} \\ $$$$\:\:\:\:\:\:\:\:\:{prove}\::\:\:\:{m}^{\varphi\left({n}\right)} +{n}^{\varphi\left({m}\right)} \overset{{mn}} {\equiv}\mathrm{1} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\varphi\left({n}\right)=\mid\left\{{x}\in\mathbb{N}\mid\:{x}<{n}\:,\:\left({x},{n}\right)=\mathrm{1}\right\}\mid \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:.{m}.{n}. \\ $$ Answered by…

Known-set-A-R-not-empty-If-Sup-A-Inf-A-then-set-A-is-

Question Number 55633 by gunawan last updated on 01/Mar/19 $$\mathrm{Known}\:\mathrm{set}\:{A}\subseteq\mathbb{R}\:\mathrm{not}\:\mathrm{empty}, \\ $$$$\mathrm{If}\:\mathrm{Sup}\:{A}=\mathrm{Inf}\:{A},\:\mathrm{then}\:\mathrm{set}\:{A}\:\mathrm{is}.. \\ $$ Answered by arcana last updated on 18/Jun/19 $$\mathrm{definition} \\ $$$$\forall{x}\in\mathrm{A},\:\mathrm{Inf}\:\mathrm{A}\:\leqslant\:{x}\:\leqslant\:\mathrm{Sup}\:\mathrm{A} \\…

Q-G-V-E-is-a-graph-such-that-V-G-20-G-8-G-3-find-the-value-of-q-max-q-min-q-E-G-

Question Number 185890 by mnjuly1970 last updated on 29/Jan/23 $$ \\ $$$$\:\:{Q}:\:\:\:\:\:{G}\left(\:{V}\:,\:{E}\:\right)\:\:{is}\:{a}\:{graph}\:,\:{such}\:{that} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\mid\:\:{V}\:\left({G}\:\right)\mid\:=\:\mathrm{20}\:,\:\:\Delta\:\left(\:{G}\:\right)=\:\mathrm{8}\:,\:\:\delta\:\left({G}\:\right)=\mathrm{3} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:{find}\:\:{the}\:{value}\:{of}\:\:,\:\:{q}_{\:{max}} \:−\:{q}_{\:{min}} \:=\:? \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:{q}\:=\:\mid\:{E}\:\left({G}\:\right)\mid\:\: \\ $$ Answered by MrGaster…

find-element-of-set-S-x-3-3x-2-2-2x-1-Z-for-x-Z-

Question Number 119487 by liberty last updated on 25/Oct/20 $${find}\:{element}\:{of}\:{set}\:{S}\:=\:\left\{\:\frac{{x}^{\mathrm{3}} −\mathrm{3}{x}^{\mathrm{2}} +\mathrm{2}}{\mathrm{2}{x}+\mathrm{1}}\:\in\:\mathbb{Z}\:{for}\:{x}\in\mathbb{Z}\:\right\} \\ $$ Answered by floor(10²Eta[1]) last updated on 25/Oct/20 $$\mathrm{2x}+\mathrm{1}\mid\mathrm{x}^{\mathrm{3}} −\mathrm{3x}^{\mathrm{2}} +\mathrm{2}\Leftrightarrow \\…

let-d-be-an-application-d-R-2-R-d-x-y-ln-1-x-y-1-x-y-shown-that-d-is-a-distance-on-R-2-please-help-especially-on-triangular-inequality-

Question Number 119401 by cantor last updated on 24/Oct/20 $$\boldsymbol{{let}}\:\boldsymbol{{d}}\:\boldsymbol{{be}}\:\boldsymbol{{an}}\:\boldsymbol{{application}} \\ $$$$\boldsymbol{{d}}:\mathbb{R}^{\mathrm{2}} \rightarrow\mathbb{R}_{+} \\ $$$$\boldsymbol{{d}}\left(\boldsymbol{{x}},\boldsymbol{{y}}\right)=\boldsymbol{{ln}}\left(\mathrm{1}+\frac{\mid\boldsymbol{{x}}−\boldsymbol{{y}}\mid}{\mathrm{1}+\mid\boldsymbol{{x}}−\boldsymbol{{y}}\mid}\right) \\ $$$$\boldsymbol{{shown}}\:\boldsymbol{{that}}\:\boldsymbol{{d}}\:\boldsymbol{{is}}\:\boldsymbol{{a}}\:\boldsymbol{{distance}} \\ $$$$\boldsymbol{{on}}\:\mathbb{R}^{\mathrm{2}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{{please}}\:\boldsymbol{{help}}\: \\ $$$$\:\bigstar\boldsymbol{{especially}}\:\boldsymbol{{on}}\:\boldsymbol{{triangular}} \\ $$$$\boldsymbol{{inequality}}…