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Learning Outcomes. Mahasiswa dapat menerangkan tentang aljabar proposisi dan sifat kebenaran pernyataan operator & sifat-sifat proposisi beserta contoh penerapannya. Outline Materi:. Pengertian Aljabar Prosposisi Konsep dasar Aljabar Proposisi Sifat-sifat kebenaran Contoh permasalahan.

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Learning outcomes
Learning Outcomes

  • Mahasiswa dapat menerangkan tentang aljabar proposisi dan sifat kebenaran pernyataan operator & sifat-sifat proposisi beserta contoh penerapannya.


Outline materi
Outline Materi:

  • Pengertian Aljabar Prosposisi

  • Konsep dasar Aljabar Proposisi

  • Sifat-sifat kebenaran

  • Contoh permasalahan


Pengertian aljabar proposisi
Pengertian Aljabar Proposisi

  • Proposisi adalah suatu pernyataan gabungan

  • p,q,.. merupakan variabel, maka proposisi dapat ditulis seperti: P(p,q,r…)

  • Nilai kebenarannya diketahui, bila kebenaran variabelnya diketahui

  • Penentuan nilai kebenarannya umumnya dibuat dengan menggunakan tabel kebenaran

  • Contoh ~(p^~q);


Logika equivalent kesamaan logika
Logika Equivalent (kesamaan logika)

  • Dua proposisi yang memiliki nilai tabel kebenaran yang sama

  • Contoh

    • ~ (p ^ q) = ~p v ~q

    • (p v q) ^ q = (p ^ q) v q

    • (~p v q) ^ p = p ^ q

    • (p ^ q) v r = (p v r) ^ (q v r)


Aljabar proposisi
Aljabar Proposisi

  • Hukum yg berlaku di dalam proposisi

  • Idempotent; pvp=p, p^p=p

  • Associative; (pvq)vr = pv(qvr),

    (p^q)^r = p^(q^r)

  • Commutative; pvq = qvp, p^q = q^p

  • Distributive; pv(q^r)=(pvq)^(pvr),

    p^(qvr)=(p^q)v(p^r)

  • Identity; pvf = p, p^t=p, pvt=t, p^f=f


Aljabar proposisi 2
Aljabar Proposisi (2)

  • Complement; pv~p=t, p^~p=f, ~t=f, ~f=t

  • Involution; ~~p=p

  • DeMorgans; ~(pvq)=~p ^ ~q, ~(p^q)=~pv~q.



Aljabar proposisi 4
Aljabar Proposisi (4)

~(~pq)(pr) = (p~q)(pr),

De’Morgan dan involusi = [(p~q)p][(p~q)r], distributive = p(~qp)(pr)(~qr), distributive= p(~qr), absorbsi.


Terima kasih,

Semoga berhasil


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