ข้อสอบ PAT 1 - เมษายน 2557

ข้อ 1

สำหรับเซต S ใดๆ ให้ n left parenthesis S right parenthesis แทนจำนวนสมาชิกของเซต S กำหนดให้ begin mathsize 12px style ด ึ งต ั วร ่ วม space A space semicolon thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space equals open square brackets A times open parentheses B to the power of negative 1 end exponent B plus A to the power of negative 1 end exponent B close parentheses close square brackets to the power of negative 1 end exponent space space space space space space space ด ึ งต ั วร ่ วม space B space semicolon thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space equals open square brackets A times open parentheses B to the power of negative 1 end exponent plus A to the power of negative 1 end exponent close parentheses times B close square brackets to the power of negative 1 end exponent space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space bold โดย space open parentheses A B C close parentheses to the power of negative 1 end exponent equals C to the power of negative 1 end exponent B to the power of negative 1 end exponent A to the power of negative 1 end exponent space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space thin space equals B to the power of negative 1 end exponent times open parentheses B to the power of negative 1 end exponent plus A to the power of negative 1 end exponent close parentheses to the power of negative 1 end exponent times A to the power of negative 1 end exponent space space space space สล ั บท ี่ การบวก space semicolon thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space equals B to the power of negative 1 end exponent times open parentheses A to the power of negative 1 end exponent plus B to the power of negative 1 end exponent close parentheses to the power of negative 1 end exponent times A to the power of negative 1 end exponent end style แทนเอกภพสัมพัทธ์ ถ้า A comma B spaceและ C เป็นสับเซตใน begin mathsize 12px style ด ึ งต ั วร ่ วม space A space semicolon thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space equals open square brackets A times open parentheses B to the power of negative 1 end exponent B plus A to the power of negative 1 end exponent B close parentheses close square brackets to the power of negative 1 end exponent space space space space space space space ด ึ งต ั วร ่ วม space B space semicolon thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space equals open square brackets A times open parentheses B to the power of negative 1 end exponent plus A to the power of negative 1 end exponent close parentheses times B close square brackets to the power of negative 1 end exponent space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space bold โดย space open parentheses A B C close parentheses to the power of negative 1 end exponent equals C to the power of negative 1 end exponent B to the power of negative 1 end exponent A to the power of negative 1 end exponent space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space thin space equals B to the power of negative 1 end exponent times open parentheses B to the power of negative 1 end exponent plus A to the power of negative 1 end exponent close parentheses to the power of negative 1 end exponent times A to the power of negative 1 end exponent space space space space สล ั บท ี่ การบวก space semicolon thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space equals B to the power of negative 1 end exponent times open parentheses A to the power of negative 1 end exponent plus B to the power of negative 1 end exponent close parentheses to the power of negative 1 end exponent times A to the power of negative 1 end exponent end style โดยที่n left parenthesis A right parenthesis equals 2 left parenthesis n left parenthesis B right parenthesis right parenthesis equals 3 left parenthesis n left parenthesis C right parenthesis right parenthesis space comma space n left parenthesis A union B union C right parenthesis equals 15 , n left parenthesis A intersection B intersection C right parenthesis equals 2  ถ้า n left parenthesis A minus B right parenthesis equals 8 comma n left parenthesis B minus C right parenthesis equals 4 spaceและ n left parenthesis A minus C right parenthesis equals 9 แล้ว n left parenthesis left parenthesis A union B right parenthesis minus C right parenthesis เท่ากับข้อใดต่อไปนี้

รีวิว - เสียงตอบรับจากผู้เรียน
รีวิวสอบติด
รีวิวสอบติด
รีวิวสอบติด
รีวิวสอบติด
รีวิวสอบติด
รีวิวสอบติด
รีวิวสอบติด
รีวิวสอบติด
รีวิวสอบติด
รีวิวสอบติด
รีวิวสอบติด

เฉลยข้อสอบ

begin mathsize 12px style จากน ิ ยามของเมตร ิ กซ ์ space space space space space space space space space open parentheses A B close parentheses to the power of negative 1 end exponent equals A to the power of negative 1 end exponent B to the power of negative 1 end exponent space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space open parentheses A B C close parentheses to the power of negative 1 end exponent equals C to the power of negative 1 end exponent B to the power of negative 1 end exponent A to the power of negative 1 end exponent space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space A times A to the power of negative 1 end exponent equals A to the power of negative 1 end exponent times A equals I space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space B times B to the power of negative 1 end exponent equals B to the power of negative 1 end exponent times B equals I end style

begin mathsize 12px style จากโจทย ์ space space straight n open parentheses straight A minus straight B close parentheses equals 8 จะได ้ space space space space space space space space space space space space space space space straight a plus straight d equals 8 rightwards arrow box enclose 1 จากโจทย ์ space space straight n open parentheses straight B minus straight C close parentheses equals 4 จะได ้ space space space space space space space space space space space space space space space space straight b plus straight c equals 4 rightwards arrow box enclose 2 จากโจทย ์ thin space space space straight n open parentheses straight A minus straight C close parentheses equals 9 จะได ้ space space space space space space space space space space space space space space space space straight a plus straight b equals 9 rightwards arrow box enclose 3 end style

begin mathsize 12px style ด ึ งต ั วร ่ วม space A space semicolon thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space equals open square brackets A times open parentheses B to the power of negative 1 end exponent B plus A to the power of negative 1 end exponent B close parentheses close square brackets to the power of negative 1 end exponent space space space space space space space ด ึ งต ั วร ่ วม space B space semicolon thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space equals open square brackets A times open parentheses B to the power of negative 1 end exponent plus A to the power of negative 1 end exponent close parentheses times B close square brackets to the power of negative 1 end exponent space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space bold โดย space open parentheses A B C close parentheses to the power of negative 1 end exponent equals C to the power of negative 1 end exponent B to the power of negative 1 end exponent A to the power of negative 1 end exponent space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space thin space equals B to the power of negative 1 end exponent times open parentheses B to the power of negative 1 end exponent plus A to the power of negative 1 end exponent close parentheses to the power of negative 1 end exponent times A to the power of negative 1 end exponent space space space space สล ั บท ี่ การบวก space semicolon thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space equals B to the power of negative 1 end exponent times open parentheses A to the power of negative 1 end exponent plus B to the power of negative 1 end exponent close parentheses to the power of negative 1 end exponent times A to the power of negative 1 end exponent end style​

begin mathsize 12px style จากโจทย ์ space space thin space thin space thin space thin space thin space thin space thin space thin space thin space straight n open parentheses straight A close parentheses equals 3 open parentheses straight n open parentheses straight C close parentheses close parentheses จะได ้ space space straight a plus straight b plus straight d plus 2 equals 3 open parentheses straight d plus straight e plus straight f plus 2 close parentheses space space space space space space space space open parentheses straight a plus straight b close parentheses plus straight d plus 2 equals 3 straight d plus 3 open parentheses straight e plus straight f close parentheses plus 6 space space space semicolon space จาก space box enclose 3 space comma space box enclose 4 จะได ้ space space space space space space space space 9 plus straight d plus 2 equals 3 straight d plus 3 open parentheses 1 close parentheses plus 6 space space space space space space space space space space space space space space space space space space space space space straight d plus 11 equals 3 straight d plus 9 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space 2 equals 2 straight d space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space straight d equals 1 space space space space space semicolon space แทนใน space box enclose 1 end style

begin mathsize 12px style ด ึ งต ั วร ่ วม space A space semicolon thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space equals open square brackets A times open parentheses B to the power of negative 1 end exponent B plus A to the power of negative 1 end exponent B close parentheses close square brackets to the power of negative 1 end exponent space space space space space space space ด ึ งต ั วร ่ วม space B space semicolon thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space equals open square brackets A times open parentheses B to the power of negative 1 end exponent plus A to the power of negative 1 end exponent close parentheses times B close square brackets to the power of negative 1 end exponent space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space bold โดย space open parentheses A B C close parentheses to the power of negative 1 end exponent equals C to the power of negative 1 end exponent B to the power of negative 1 end exponent A to the power of negative 1 end exponent space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space thin space equals B to the power of negative 1 end exponent times open parentheses B to the power of negative 1 end exponent plus A to the power of negative 1 end exponent close parentheses to the power of negative 1 end exponent times A to the power of negative 1 end exponent space space space space สล ั บท ี่ การบวก space semicolon thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space equals B to the power of negative 1 end exponent times open parentheses A to the power of negative 1 end exponent plus B to the power of negative 1 end exponent close parentheses to the power of negative 1 end exponent times A to the power of negative 1 end exponent end style

begin mathsize 12px style จากน ิ ยามของเมตร ิ กซ ์ space space space space space space space space space open parentheses A B close parentheses to the power of negative 1 end exponent equals A to the power of negative 1 end exponent B to the power of negative 1 end exponent space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space open parentheses A B C close parentheses to the power of negative 1 end exponent equals C to the power of negative 1 end exponent B to the power of negative 1 end exponent A to the power of negative 1 end exponent space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space A times A to the power of negative 1 end exponent equals A to the power of negative 1 end exponent times A equals I space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space B times B to the power of negative 1 end exponent equals B to the power of negative 1 end exponent times B equals I end style

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