Book Store

Download books and chapters from book store.
Currently only available for
CBSE Gujarat Board Haryana Board

Previous Year Papers

Download the PDF Question Papers Free for off line practice and view the Solutions online.
Currently only available for
Class 10 Class 12

ગણક્રિયાઓ

જો $bold A bold space bold equals bold space open curly brackets bold x bold divided by bold x bold space bold element of bold space bold Z bold comma bold space bold x to the power of bold 2 bold space bold minus bold space bold x bold space bold equals bold space bold 0 close curly brackets bold comma bold space bold B bold space bold equals bold space open curly brackets bold x bold divided by bold x bold space bold element of bold space bold N bold comma bold space bold 1 bold space bold less-than or slanted equal to bold space bold x bold space bold less-than or slanted equal to bold 4 close curly brackets$ , તો $bold A bold space bold subset of bold space bold B$ કહી શકાય ? શા માટે ?

ગણ A = {1, 2, 3}ના ઉપગણોની સંખ્યા શોધો તથા ગણ Aના તમામ ઉપગણો લખો.

જો U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} , A = {1, 2, 4, 6, 8}, તો A’ શોધો અને બતાવો કે $bold A bold space bold union bold space bold A bold apostrophe bold space bold equals bold space bold U bold.$

U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} અને A = {1, 2, 4, 6, 8}

હવે, $bold A bold apostrophe bold space bold equals bold space open curly brackets bold x bold divided by bold x bold space bold element of bold space bold U bold comma bold space bold x bold space bold not an element of bold space bold A close curly brackets$

એટલે કે Uમાં હોય, પરંતુ ગણ Aમાં ન હોય તેવા ઘટકો 3, 5, 7, 9 અને 10 છે.

A’ = {3, 5, 7, 9, 10}

હવે,

$bold A bold space bold union bold space bold A bold apostrophe bold space bold equals bold space bold left curly bracket bold 1 bold comma bold space bold 2 bold comma bold space bold 4 bold comma bold space bold 6 bold comma bold space bold 8 bold right curly bracket bold space bold union bold space bold left curly bracket bold 3 bold comma bold space bold 5 bold comma bold space bold 7 bold comma bold space bold 9 bold comma bold space bold 10 bold right curly bracket bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold equals bold space bold left curly bracket bold 1 bold comma bold space bold 2 bold comma bold space bold 3 bold comma bold space bold 4 bold comma bold space bold 5 bold comma bold space bold 6 bold comma bold space bold 7 bold comma bold space bold 8 bold comma bold space bold 9 bold comma bold space bold 10 bold right curly bracket bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold equals bold space bold U$

$bold therefore bold space bold A bold space bold union bold space bold A bold apostrophe bold space bold equals bold space bold U$ સાબિત થાય છે.

નીચે આપેલ ગણને સમાન ગણ અથવા સામ્ય ગણમાં વર્ગીકૃત કરો :
$open parentheses bold 1 close parentheses bold space bold A bold space bold equals bold space open curly brackets bold x bold divided by bold x bold space bold element of bold space bold N bold comma bold space bold x bold space bold less-than or slanted equal to bold space bold 7 close curly brackets bold space bold space bold space bold space bold space bold B bold space bold equals bold space open curly brackets bold x bold divided by bold x bold space bold element of bold space bold Z bold comma bold space bold minus bold 3 bold space bold less-than or slanted equal to bold space bold x bold space bold less-than or slanted equal to bold space bold 3 close curly brackets open parentheses bold 2 close parentheses bold space bold A bold space bold equals bold space open curly brackets bold x bold divided by bold x bold space bold element of bold space bold N bold comma bold space bold x bold space bold એ bold space bold 2 bold space bold ન ો bold space bold ગ ુ ણક bold space bold છ ે bold comma bold space bold x bold space bold less than bold space bold 10 close curly brackets bold space bold space bold space bold space bold space bold B bold space bold equals bold space open curly brackets bold x bold divided by bold x bold space bold element of bold space bold N bold comma bold space bold x bold space bold એ bold space bold 10 bold થ ી bold space bold ન ા ન ી bold space bold ય ુ ગ ્ મ bold space bold પ ્ ર ા ક ૃ ત િ ક bold space bold સ ં ખ ્ ય ા bold space bold છ ે bold. close curly brackets$

નીચેર આપેલ ગણને ખાલી ગણ કે એકાકી ગણમાં વર્ગીકૃત કરો :
$open parentheses bold 1 close parentheses bold space bold A bold space bold equals bold space open curly brackets bold x bold divided by bold x bold space bold element of bold space bold Z bold comma bold space bold x bold space bold plus bold space bold 1 bold space bold equals bold space bold 0 close curly brackets open parentheses bold 2 close parentheses bold space bold B bold space bold equals bold space open curly brackets bold x bold divided by bold x bold space bold element of bold space bold N bold comma bold space bold x to the power of bold 2 bold space bold minus bold space bold 1 bold space bold equals bold space bold 0 close curly brackets open parentheses bold 3 close parentheses bold space bold C bold space bold equals bold space open curly brackets bold x bold divided by bold x bold space bold element of bold space bold N bold comma bold space bold x bold space bold એ bold space bold 13 bold space bold અન ે bold space bold 17 bold space bold વચ ્ ચ ે ન ી bold space bold અવ િ ભ ા જ ્ ય bold space bold સ ં ખ ્ ય ા close curly brackets$

Switch

Chapter Chosen

Book Chosen

Subject Chosen

Book Store

Previous Year Papers

ગણક્રિયાઓ

Switch