โจทย์ปัญหาเรื่องเซต ข้อที่ 1 PDF Print E-mail
Wednesday, 19 November 2008 19:50
ระดับความยาก 4/10
Ent'42 ถ้า A = {Ø , 0 ,  1 , {0} , {0,1}} และ P(A) เป็นเพาเวอร์เซต A แล้ว P(A) - A มีสมาชิกกี่ตัว

เฉลย >> 29 ตัว

โจทย์ข้อนี้ไม่ยากเลยครับแต่ต้องอาศัยความรอบคอบสักนิดหนึ่ง
ก่อนอื่นเลยต้องรู้ก่อนครับว่า P(A) มีสมาชิกกี่ตัว ก็ง่ายๆนะครับตามทฤษฎีที่เคยเรียนมา ถ้า A มีสมาชิก n ตัวแล้ว
P(A) จะมีสมาชิกทั้งหมด 2 ยกกำลัง n ตัวครับ แน่นอนครับว่าจำนวนสมาชิกของ A มีทั้งสิ้น 5 ตัว
(ใครดูไม่ออกว่ามี 5 ตัว แนะนำให้ไปอ่านเรื่องเซตใหม่อีกรอบนะครับ) ดังนั้น P(A) จะมีสมาชิกทั้งหมด 2^5 = 32 ตัวครับ
ต่อมาเราต้องหาว่า P(A) - A มีสมาชิกกี่ตัว ก็ถ้าทำตามวิธีตรงๆ ก็คือต้องเขียนการแจกแจงสมาชิกของ P(A) แล้วลบออก
ด้วย A ครับ แล้วจึงนับสมาชิกที่เหลือ แต่ทว่าเวลาในห้องสอบไม่รีรอใคร ดังนั้นผมจึงแนะนำว่าให้เขียนตัวที่ซ้ำกันก็พอครับ
เพราะเราจะนำจำนวนทั้งหมดของ P(A) มาหักออกกับจำนวนสมาชิกของ A ที่ซ้ำกัน จากการวิเคราะห์ของเรา
เมื่อลองคิดดูแล้วก็จะได้ว่ามีสมาชิกของ P(A)ที่เหมือนกับ A อยู่ทั้งสิ้น 3 ตัว นั่นคือ {0} , {0,1} และ Ø ครับ
ดังนั้น จำนวนของ P(A) - A จึงมีทั้งสิ้น 29 ตัวครับ

หมายเหตุ : สัญลักษณ์ ^ คือการยกกำลังนะครับ

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โฮ้ว มะค่อยรู้เรื่อวงอ่าครับ ยากดี เเต่ละข้ออ่านะ ครับ 55^^ ข้อนี้ก้อยังทำมะไ ลองเเละ จาให้ดี พี่ลอง เเสดงวิธีทำหน่อยสิครับ ผมเขียนสับเซตมันได้ 27อ่าครับ 55+^^
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avatar jeux.fr
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Solid write up! thank you so much for this info!
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avatar jeux news
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Excellent piece! thanks for this info!
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avatar jeux news
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Solid piece! thanks for this info!
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avatar grande taille femme
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Solid blog post! thanks so much for this info!
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avatar grande taille femme
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Solid blog post! thank you so much for this info!
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avatar stagevu
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Solid post! thank you so much for this information!
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avatar stagevu
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Fantastic piece! thank you for this info!
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avatar Getbetterlife.com
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Good article!
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avatar riad luxe
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Fantastic write up! thanks for this information!
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avatar riad luxe
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Excellent post! thank you for this information!
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avatar riad anya marrakech
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Excellent write up! thank you for this information!
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avatar riad anya marrakech
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Great blog post! thanks so much for this information!
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avatar zshare
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Excellent post! thank you for this information!
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avatar zshare
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Fantastic post! thanks so much for this information!
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avatar streamiz
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Great piece! thanks for this info!
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avatar streamiz
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Solid article! thanks for this information!
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avatar duckload
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Solid write up! thank you so much for this information!
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avatar duckload
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Amazing write up! thank you for this information!
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