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Category: Set Theory

How-many-ordered-triplets-x-y-z-of-positive-integer-satisfy-lcm-x-y-72-lcm-x-z-600-and-lcm-y-z-900-

Question Number 19634 by Tinkutara last updated on 13/Aug/17 $$\mathrm{How}\:\mathrm{many}\:\mathrm{ordered}\:\mathrm{triplets}\:\left({x},\:{y},\:{z}\right)\:\mathrm{of} \\ $$$$\mathrm{positive}\:\mathrm{integer}\:\mathrm{satisfy}\:\mathrm{lcm}\left({x},\:{y}\right)\:=\:\mathrm{72}, \\ $$$$\mathrm{lcm}\left({x},\:{z}\right)\:=\:\mathrm{600}\:\mathrm{and}\:\mathrm{lcm}\left({y},\:{z}\right)\:=\:\mathrm{900}? \\ $$ Answered by Tinkutara last updated on 16/Oct/17 Terms of…

6-1-5-1-2-1-3-x-How-to-write-x-in-standard-form-

Question Number 13200 by Joel577 last updated on 16/May/17 $$\sqrt[{\sqrt[{\sqrt[{\sqrt{\mathrm{3}}}]{\mathrm{2}}}]{\mathrm{5}}}]{\mathrm{6}}\:=\:{x} \\ $$$$\mathrm{How}\:\mathrm{to}\:\mathrm{write}\:{x}\:\mathrm{in}\:\mathrm{standard}\:\mathrm{form}? \\ $$ Answered by ajfour last updated on 16/May/17 $${x}=\mathrm{6}^{\left[\frac{\mathrm{1}}{\mathrm{5}^{\left(\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{1}/\sqrt{\mathrm{3}}} }\right)} }\right]} \:…

A-0-2-4-6-8-10-B-0-1-3-4-6-7-9-C-1-2-4-5-7-8-10-A-B-B-C-

Question Number 245 by 123456 last updated on 25/Jan/15 $$\mathrm{A}=\left\{\mathrm{0},\mathrm{2},\mathrm{4},\mathrm{6},\mathrm{8},\mathrm{10}\right\} \\ $$$$\mathrm{B}=\left\{\mathrm{0},\mathrm{1},\mathrm{3},\mathrm{4},\mathrm{6},\mathrm{7},\mathrm{9}\right\} \\ $$$$\mathrm{C}=\left\{\mathrm{1},\mathrm{2},\mathrm{4},\mathrm{5},\mathrm{7},\mathrm{8},\mathrm{10}\right\} \\ $$$$\mid\left(\mathrm{A}\cup\mathrm{B}\right)\cap\left(\mathrm{B}\cup\mathrm{C}\right)\mid \\ $$ Answered by mreddy last updated on 17/Dec/14…

give-the-sets-A-x-N-0-x-9-B-0-C-1-D-2-3-5-7-E-4-6-8-9-compute-A-B-A-C-A-D-A-E-where-X-number-of-elements-of-X-X-Y-x-x-X-e-x-Y-X-Y-x-x-X-e-x-Y-

Question Number 242 by 123456 last updated on 25/Jan/15 $$\mathrm{give}\:\mathrm{the}\:\mathrm{sets} \\ $$$$\mathrm{A}=\left\{{x}\in\mathbb{N}:\mathrm{0}\leqslant{x}\leqslant\mathrm{9}\right\} \\ $$$$\mathrm{B}=\left\{\mathrm{0}\right\} \\ $$$$\mathrm{C}=\left\{\mathrm{1}\right\} \\ $$$$\mathrm{D}=\left\{\mathrm{2},\mathrm{3},\mathrm{5},\mathrm{7}\right\} \\ $$$$\mathrm{E}=\left\{\mathrm{4},\mathrm{6},\mathrm{8},\mathrm{9}\right\} \\ $$$$\mathrm{compute} \\ $$$$\mid\mathrm{A}\backslash\mathrm{B}\mid+\mid\mathrm{A}\backslash\mathrm{C}\mid+\mid\mathrm{A}\backslash\mathrm{D}\mid+\mid\mathrm{A}\backslash\mathrm{E}\mid \\…

Question-12291

Question Number 12291 by 1kanika# last updated on 18/Apr/17 Answered by 433 last updated on 07/May/17 $$\begin{bmatrix}{\mathrm{0}}&{\mathrm{1}}\\{\mathrm{1}}&{\mathrm{0}}\end{bmatrix}×\begin{bmatrix}{\mathrm{0}}&{−\mathrm{1}}\\{\mathrm{1}}&{\mathrm{0}}\end{bmatrix}=\begin{bmatrix}{\mathrm{1}}&{\mathrm{0}}\\{\mathrm{0}}&{−\mathrm{1}}\end{bmatrix}={A} \\ $$$$\begin{bmatrix}{\mathrm{0}}&{−\mathrm{1}}\\{\mathrm{1}}&{\mathrm{0}}\end{bmatrix}×\begin{bmatrix}{\mathrm{0}}&{\mathrm{1}}\\{\mathrm{1}}&{\mathrm{0}}\end{bmatrix}=\begin{bmatrix}{−\mathrm{1}}&{\mathrm{0}}\\{\mathrm{0}}&{\mathrm{1}}\end{bmatrix}=−{A} \\ $$$$\begin{bmatrix}{\mathrm{0}}&{−\mathrm{1}}\\{\mathrm{1}}&{\mathrm{0}}\end{bmatrix}×\begin{bmatrix}{\mathrm{0}}&{−\mathrm{1}}\\{\mathrm{1}}&{\mathrm{0}}\end{bmatrix}=\begin{bmatrix}{−\mathrm{1}}&{\mathrm{0}}\\{\mathrm{0}}&{−\mathrm{1}}\end{bmatrix}=−{I}_{\mathrm{2}} \\ $$$$\begin{bmatrix}{\mathrm{0}}&{\mathrm{1}}\\{\mathrm{1}}&{\mathrm{0}}\end{bmatrix}^{\mathrm{2}} ={I}_{\mathrm{2}} \\…