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Author: Tinku Tara

Are-A-B-A-B-and-A-B-completely-equivalent-Simplify-A-B-A-B-to-A-B-using-set-operations-and-their-properties-

Question Number 1698 by Rasheed Ahmad last updated on 01/Sep/15 $$\bullet{Are}\:\boldsymbol{\mathrm{A}}\cup\boldsymbol{\mathrm{B}}=\boldsymbol{\mathrm{A}}\cap\boldsymbol{\mathrm{B}}\:\:{and}\:\:\boldsymbol{\mathrm{A}}=\boldsymbol{\mathrm{B}}\: \\ $$$${completely}\:{equivalent}? \\ $$$$\bullet{Simplify}\:\boldsymbol{\mathrm{A}}\cup\boldsymbol{\mathrm{B}}=\boldsymbol{\mathrm{A}}\cap\boldsymbol{\mathrm{B}}\:{to}\:\boldsymbol{\mathrm{A}}=\boldsymbol{\mathrm{B}} \\ $$$${using}\:{set}\:{operations}\:{and}\:{their} \\ $$$${properties}. \\ $$ Answered by 123456 last…

proof-that-for-two-set-A-and-B-or-give-a-counter-example-A-B-A-B-

Question Number 1694 by 123456 last updated on 01/Sep/15 $$\mathrm{proof}\:\mathrm{that}\:\mathrm{for}\:\mathrm{two}\:\mathrm{set}\:\mathrm{A}\:\mathrm{and}\:\mathrm{B}\:\left(\mathrm{or}\:\mathrm{give}\:\mathrm{a}\:\mathrm{counter}\:\mathrm{example}\right) \\ $$$$\mid\mathrm{A}\cup\mathrm{B}\mid\geqslant\mid\mathrm{A}\cap\mathrm{B}\mid \\ $$ Answered by Rasheed Soomro last updated on 01/Sep/15 $$\:\mathrm{In}\:\mathrm{the}\:\mathrm{following}\:\boldsymbol{\mathrm{A}}\:\mathrm{and}\:\boldsymbol{\mathrm{B}}\:\mathrm{are}\:\mathrm{assumed}\:\mathrm{as}\:\mathrm{finite}\:\mathrm{sets}. \\ $$$$\:\boldsymbol{\mathrm{A}}\cap\boldsymbol{\mathrm{B}}\:\subseteq\boldsymbol{\mathrm{A}}\subseteq\:\boldsymbol{\mathrm{A}}\cup\boldsymbol{\mathrm{B}}\Rightarrow\mid\boldsymbol{\mathrm{A}}\cap\boldsymbol{\mathrm{B}}\mid\leqslant\mid\boldsymbol{\mathrm{A}}\mid\leqslant\mid\boldsymbol{\mathrm{A}}\cup\boldsymbol{\mathrm{B}}\mid………..\boldsymbol{\mathrm{I}}…

Question-132762

Question Number 132762 by liberty last updated on 16/Feb/21 Answered by EDWIN88 last updated on 16/Feb/21 $$\Rightarrow\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} =\:\mathrm{9}\:\Rightarrow\mathrm{x}^{\mathrm{2}} =\mathrm{9}−\mathrm{y}^{\mathrm{2}} \\ $$$$\mathrm{Volume}\:=\:\frac{\mathrm{1}}{\mathrm{3}}\pi\mathrm{x}^{\mathrm{2}} \left(\mathrm{3}+\mathrm{y}\right)=\:\frac{\mathrm{1}}{\mathrm{3}}\pi\left(\mathrm{9}−\mathrm{y}^{\mathrm{2}} \right)\left(\mathrm{3}+\mathrm{y}\right) \\…

Given-x-y-R-x-y-0-Find-the-maximum-and-minimum-value-of-xy-4y-2-x-2-4y-2-

Question Number 132753 by liberty last updated on 16/Feb/21 $$\mathrm{Given}\:\mathrm{x},\mathrm{y}\:\in\mathbb{R}\:,\:\mathrm{x},\mathrm{y}\neq\:\mathrm{0} \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{maximum}\:\mathrm{and}\:\mathrm{minimum} \\ $$$$\mathrm{value}\:\mathrm{of}\:\frac{\mathrm{xy}−\mathrm{4y}^{\mathrm{2}} }{\mathrm{x}^{\mathrm{2}} +\mathrm{4y}^{\mathrm{2}} }\: \\ $$ Commented by mr W last updated…