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Matematika Diskrit - Matematika Diskrit 1

Matematika Diskrit - Matematika Diskrit 1

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From which premise can we validly conclude "∃x P(x)" using Existential Generalization?

P(c) for some specific element c

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Which of the following is an example of a constructive existence proof?

Proving there exist irrational numbers x and y such that xʸ is rational without specifying which ones

Proving that a solution must exist but not finding it explicitly

Showing that if a solution doesn't exist, we get a contradiction

Showing 1729 = 10³ + 9³ = 12³ + 1³ as an example of a number that is the sum of cubes in two ways

Assuming no such number exists and deriving a contradiction

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What is the correct negation of the statement "All students passed the exam" where P(x) means "x passed the exam" and the domain is all students?

All students did not pass the exam

Some student passed the exam

Some student did not pass the exam

All students failed the exam

No student passed the exam

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Which of the following best describes a direct proof of the statement "If n is odd, then n² is odd"?

Assume n is not odd and show n² is not odd

Assume n is odd, so n = 2k + 1 for some integer k, then show n² = 2(2k² + 2k) + 1 is odd

Show examples where n is odd and n² is odd

Assume n is even and n² is odd, then derive a contradiction

Assume n² is even and show n must be even

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Ada berapa cara berbeda untuk memilih komite yang terdiri dari 3 anggota DPR dan 3 anggota MPR? Dimana ada 100 anggota DPR dan 435 anggota MPR.

435.434.433 + 100.99.98

C(435,3).C(100,3)

C(435,3)+C(100,3)

P(435,3).P(100,3)

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Sebuah asrama memiliki 40 siswa yang terdiri dari 8 siswa kelas 1, 12 siswa kelas 2, dan 20 siswa kelas 3. Ada berapa cara untuk membentuk komite yang terdiri dari 5 siswa dari kelas yang sama?

C(12,5).C(8,5).C(20,5)

C(12,5) + C(8,5) + C(20,5)

P(12,5).P(8,5).P(20,5)

P(12,5) + P(8,5) + P(20,5)

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Ada berapa plat nomor kendaraan yang tersedia jika polanya terdiri dari 3 huruf kapital yang tidak boleh diulang dan diikuti 3 angka yang dapat diulang?

26.25.24.10.9.8

C(26,3).C(10,3)

26.25.24.10.10.10

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Anda memiliki 12 bola, nomor 1 sampai 12, yang akan diletakan ke dalam 4 kotak, nomor 1 sampai 4. Jika kotak di awal dalam keadaan kosong, ada berapa cara 12 bola tsb dapat didistribusikan ke 4 kotak tsb?

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Ada berapa password berbeda yang dapat dibentuk dari 6 karakter yang masing-masing bisa berupa huruf kapital/besar, huruf kecil, atau angka, dan setidaknya 1 digit berupa angka?

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Soal 4

Jawaban B)

Jawaban C)

Jawaban D)

Jawaban A)

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