Saturday, May 18, 2013

Logika matematika

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
Wahhh matematika mungkin dalam benak anda itu suatu yang menyulit kan. waow. Tapi Berbeda Dengan logika metematika . . penasaran ini penjelasanya.

 Logika matematika adalah cabang logika dan matematika yang mengandung kajian matematis logika dan aplikasi kajian ini pada bidang-bidang lain di luar matematika. Logika matematika berhubungan erat dengan ilmu komputer dan logika filosofis. Tema utama dalam logika matematika antara lain adalah kekuatan ekspresif
dari logika formal dan kekuatan deduktif dari sistem pembuktian formal. Logika matematika sering dibagi ke dalam cabang-cabang dari teori himpunan, teori model, teori rekursi, teori pembuktian, serta matematika konstruktif. Bidang-bidang ini memiliki hasil dasar logika yang serupa.


Hukum logika

  1. Hukum komutatif
    • p ∧ q ≡ q ∧ p
    • p ∨ q ≡ q ∨ p
  2. Hukum asosiatif
    • (p ∧ q) ∧ r ≡ p ∧ (q ∧ r)
    • (p ∨ q) ∨ r ≡ p ∨ (q ∨ r)
  3. Hukum distributif
    • p ∧ (q ∨ r) ≡ (p ∧ q) ∨ (p ∧ r)
    • p ∨ (q ∧ r) ≡ (p ∨ q) ∧ (p ∨ r)
  4. Hukum identitas
    • p ∧ B ≡ p
    • p ∨ S ≡ p
  5. Hukum ikatan
    • p ∧ S ≡ S
    • p ∨ B ≡ B
  6. Hukum negasi
    • p ∧ ~p ≡ B
    • p ∨ ~p ≡ S
  7. Hukum negasi ganda
    • ~(~p) ≡ p
  8. Hukum idempotent
    • p ∧ p ≡ p
    • p ∨ p ≡ p
  9. Hukum De Morgan
    • ~(p ∧ q) ≡ ~p ∨ ~q
    • ~(p ∨ q) ≡ ~p ∧ ~q
  10. Hukum penyerapan
    • p ∧ (p ∨ q) ≡ p
    • p ∨ (p ∧ q) ≡ p
  11. Negasi B dan S
    • ~B ≡ S
    • ~S ≡ B 
     Copyright ; wikipedia
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