find-the-value-of-b-and-B-U-A-B-if-U-1-2-3-4-5-6-7-8-9-10-A-2-4-5-6-B-1-5-8-9-is-a-unoin-

Question Number 7323 by rohit meena last updated on 23/Aug/16

$${find}\:{the}\:{value}\:{of} \\ $$$$\Delta'\Lambda\:{b}\:{and}\:\left({B}'{U}\:{A}\right)\:\boldsymbol{\Lambda}\:{B} \\ $$$${if}\:{U}=\left\{\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{4},\mathrm{5},\mathrm{6},\mathrm{7},\mathrm{8},\mathrm{9},\mathrm{10}\right\} \\ $$$${A}=\left\{\mathrm{2},\mathrm{4},\mathrm{5},\mathrm{6}\right\} \\ $$$${B}=\left\{\mathrm{1},\mathrm{5},\mathrm{8},\mathrm{9}\right\} \\ $$$$\Lambda\:{is}\:{a}\:{unoin} \\ $$

Commented by rohit meena last updated on 23/Aug/16

$${answer}\:{please} \\ $$

Commented by Rasheed Soomro last updated on 24/Aug/16

$${What}\:{is}\:\Delta? \\ $$

Commented by rohit meena last updated on 24/Aug/16

$${A}\:{hai} \\ $$

Commented by rohit meena last updated on 24/Aug/16

$${A}\:{hai} \\ $$

Answered by Rasheed Soomro last updated on 24/Aug/16

$$\:{U}=\left\{\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{4},\mathrm{5},\mathrm{6},\mathrm{7},\mathrm{8},\mathrm{9},\mathrm{10}\right\},{A}=\left\{\mathrm{2},\mathrm{4},\mathrm{5},\mathrm{6}\right\},\:{B}=\left\{\mathrm{1},\mathrm{5},\mathrm{8},\mathrm{9}\right\} \\ $$$$\left({i}\right)\:{A}'\cap{B}\:\:\:\:\:\:\left({ii}\right)\:\left({B}\:'\cup{A}\right)\cap{B} \\ $$$$−−−−−−−−−−−−−−−−−−−−−−−−−− \\ $$$${A}'\cap{B}=\left({U}−{A}\right)\cap{B} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:=\left(\left\{\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{4},\mathrm{5},\mathrm{6},\mathrm{7},\mathrm{8},\mathrm{9},\mathrm{10}\right\}−\left\{\mathrm{2},\mathrm{4},\mathrm{5},\mathrm{6}\right\}\right)\cap\left\{\mathrm{1},\mathrm{5},\mathrm{8},\mathrm{9}\right\} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:=\left\{\mathrm{1},\mathrm{3},\mathrm{7},\mathrm{8},\mathrm{9},\mathrm{10}\right\}\cap\left\{\mathrm{1},\mathrm{5},\mathrm{8},\mathrm{9}\right\} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:=\left\{\mathrm{1},\mathrm{8},\mathrm{9}\right\} \\ $$$$\left({B}\:'\cup{A}\right)\cap{B} \\ $$$$ \\ $$$${Way}#\mathrm{1}:\:{First}\:{simplify}\:{using}\:{properties}. \\ $$$$\left({B}\:'\cup{A}\right)\cap{B}=\left({B}\:'\cap{B}\right)\cup\left({A}\cap{B}\right)\:\left[\cap\:{is}\:{right}-{distributive}\:{over}\:\cup\right] \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\phi\cup\left({A}\cap{B}\right)\:\:\left[{B}\:'\cap{B}=\phi\right] \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:={A}\cap{B} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\left\{\mathrm{2},\mathrm{4},\mathrm{5},\mathrm{6}\right\}\cap\left\{\mathrm{1},\mathrm{5},\mathrm{8},\mathrm{9}\right\} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\left\{\mathrm{5}\right\} \\ $$$$ \\ $$$${Way}#\mathrm{2}:{Using}\:\:{sets}\:{directly}.\: \\ $$$$\:\:\:\:{B}\:'={U}−{B}=\left\{\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{4},\mathrm{5},\mathrm{6},\mathrm{7},\mathrm{8},\mathrm{9},\mathrm{10}\right\}−\left\{\mathrm{1},\mathrm{5},\mathrm{8},\mathrm{9}\right\} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\left\{\mathrm{2},\mathrm{3},\mathrm{4},\mathrm{6},\mathrm{7},\mathrm{10}\right\} \\ $$$$\left({B}\:'\cup{A}\right)\cap{B}=\left(\left\{\mathrm{2},\mathrm{3},\mathrm{4},\mathrm{6},\mathrm{7},\mathrm{10}\right\}\cup\left\{\mathrm{2},\mathrm{4},\mathrm{5},\mathrm{6}\right\}\right)\cap\left\{\mathrm{1},\mathrm{5},\mathrm{8},\mathrm{9}\right\} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\left\{\mathrm{2},\mathrm{3},\mathrm{4},\mathrm{5},\mathrm{6},\mathrm{7},\mathrm{10}\right\}\cap\left\{\mathrm{1},\mathrm{5},\mathrm{8},\mathrm{9}\right\} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\left\{\mathrm{5}\right\} \\ $$$$ \\ $$

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