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-

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Question Number 242 by 123456 last updated on 25/Jan/15

$$\mathrm{give}\mathrm{the}\mathrm{sets}$$$$\mathrm{A}=\{x\in \mathbb{N}:0⩽x⩽9\}$$$$\mathrm{B}=\left\{0\right\}$$$$\mathrm{C}=\left\{1\right\}$$$$\mathrm{D}=\{2,3,5,7\}$$$$\mathrm{E}=\{4,6,8,9\}$$$$\mathrm{compute}$$$$\mid \mathrm{A}\mathrm{\setminus }\mathrm{B}\mid +\mid \mathrm{A}\mathrm{\setminus }\mathrm{C}\mid +\mid \mathrm{A}\mathrm{\setminus }\mathrm{D}\mid +\mid \mathrm{A}\mathrm{\setminus }\mathrm{E}\mid$$$$\mathrm{where}$$$$\mid \mathrm{X}\mid =\mathrm{number}\mathrm{of}\mathrm{elements}\mathrm{of}\mathrm{X}$$$$\mathrm{X}\mathrm{\setminus }\mathrm{Y}=\{x:x\in \mathrm{X}\mathbf{e}x\notin \mathrm{Y}\}$$$$\mathrm{X}-\mathrm{Y}=\{x:x\in \mathrm{X}\mathbf{e}x\notin \mathrm{Y}\}$$

Answered by prakash jain last updated on 17/Dec/14

$$\mid \mathrm{A}\mathrm{\setminus }\mathrm{B}\mid =9$$$$\mid \mathrm{A}\mathrm{\setminus }\mathrm{C}\mid =9$$$$\mid \mathrm{A}\mathrm{\setminus }\mathrm{D}\mid =6$$$$\mid \mathrm{A}\mathrm{\setminus }\mathrm{E}\mid =6$$$$\mid \mathrm{A}\mathrm{\setminus }\mathrm{B}\mid +\mid \mathrm{A}\mathrm{\setminus }\mathrm{C}\mid +\mid \mathrm{A}\mathrm{\setminus }\mathrm{D}\mid +\mid \mathrm{A}\mathrm{\setminus }\mathrm{E}\mid =30$$

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