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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.

ગણ A = {1, 2, 3}

અહીં ગણ Aની સંખ્ય-સંખ્યા 3 છે. n = 3

હવે, ગણ A ના ઉપગણોની સંખ્યા

$bold equals bold space bold 2 to the power of bold n bold equals bold space bold 2 to the power of bold 3 bold equals bold space bold 2 bold space bold cross times bold space bold 2 bold space bold cross times bold space bold 2 bold equals bold space bold 8$

ગણ Aના તમામ ઉપગણો

$bold empty set bold comma bold space open curly brackets bold 1 close curly brackets bold comma bold space open curly brackets bold 2 close curly brackets bold comma bold space open curly brackets bold 3 close curly brackets bold comma bold space open curly brackets bold 1 bold comma bold space bold 2 close curly brackets bold comma bold space open curly brackets bold 1 bold comma bold space bold 3 close curly brackets bold comma bold space open curly brackets bold 2 bold comma bold space bold 3 close curly brackets bold comma bold space open curly brackets bold 1 bold comma bold space bold 2 bold comma bold space bold 3 close curly brackets$

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

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

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