Let-A-B-and-C-be-three-sets-and-X-be-the-set-of-all-elements-which-belong-to-exactly-two-of-the-sets-A-B-and-C-Prove-that-X-is-equal-to-A-B-C-A-B-C-

Question Number 117597 by Ar Brandon last updated on 12/Oct/20

$$\mathrm{Let}\:\mathrm{A},\:\mathrm{B},\:\mathrm{and}\:\mathrm{C}\:\mathrm{be}\:\mathrm{three}\:\mathrm{sets}\:\mathrm{and}\:\mathrm{X}\:\mathrm{be}\:\mathrm{the}\:\mathrm{set}\:\mathrm{of}\:\mathrm{all} \\ $$$$\mathrm{elements}\:\mathrm{which}\:\mathrm{belong}\:\mathrm{to}\:\mathrm{exactly}\:\mathrm{two}\:\mathrm{of}\:\mathrm{the}\:\mathrm{sets}\:\mathrm{A},\mathrm{B} \\ $$$$\mathrm{and}\:\mathrm{C}.\:\mathrm{Prove}\:\mathrm{that}\:\mathrm{X}\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$$$\left(\mathrm{A}\cup\mathrm{B}\cup\mathrm{C}\right)−\left[\mathrm{A}\Delta\left(\mathrm{B}\Delta\mathrm{C}\right)\right] \\ $$

Commented by prakash jain last updated on 13/Oct/20

$$ \\ $$$$ \\ $$$$\mathrm{The}\:\mathrm{result}\:\mathrm{is}\:\mathrm{clear}\:\mathrm{from}\:\mathrm{venn}\:\mathrm{diagram}. \\ $$$$\mathrm{I}\:\mathrm{will}\:\mathrm{work}\:\mathrm{on}\:\mathrm{algebraic}\:\mathrm{prove}\: \\ $$

Terms of Service
Privacy Policy
Contact: info@tinkutara.com