Tugas Akhir Modul 1 Prof

TUGAS AKHIR MODUL 1 NAJAM MUDIN, S.Pd. NPM: 19051418010108 1.

Berdasarkan penjelasan tentang tautologi dan kontradiksi. Selesaikan masalah berikut ini dengan menuliskan langkah-langkahnya a.

 ⟹   ⟹  ⟹   ⟹  ∧  ⟹  ⟹  ⟹    ∧  ⟹     p q r  ⟹   ⟹   ⟹    ∧  ⟹     ⟹    ⟹   ⟹  ⟹     ⟹    ⟹  B B B B B B B B S B B B B S B S S S B S S S B S S B B B B B S B S B B B S S B B S S S S S B B B Perna!aan d"a!a# $%&an !a%!'(') dan $%&an &'n!rad"&#"

$.

 ∧ ∼ ∧  P q ∼  ∼  ∧    ∧ ∼  ∧   B B S S S B S S S S S B B B S S S B S S Perna!aan d"a!a# *er%+a&an &'n!rad"&#"

2.

 ∧  ⟹  ⟹   ∧  ∼  ∨∼  ∴ ∼  ∨∼   ∶  ⟹   ∧  1.  ∧    ⟹ 2. ∼  ∨∼    ∧  3. ∼     ∧  . ∼   #. ∼  ∨∼ 

(premis 1) (premis 2) (Hukum Demorgan) !odus "olens (Hukum Demorgan)

B S B S B B S B

B B S B B B B S

B B B B B B B S

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3.

Diket. $

 =  +   +   + ⋯  =   +  +  ! +   =   +   +    %(&) '   +   +   + ⋯ "   +   +   +   "   +   +  !  '   # +   +   + ⋯ " # +   +   +   "   #+  +    '  ! # +   +   + ⋯ " # +   +   +   "#+  +     ' $%&(' $%&)' ' ! $ %& %& %&    ' ! $ %&)'#* #*    '  ! #*  #*  ,  '  ! #*  *   +  . ,-   '  ! *  /  *  0 +   ,- Banyak ara yang dimaksud ' koeisien    dalam %(&) adalah sebagai berikut $ !  = $#4' = #25  ⟹ !" ! = 1 $2+#3*# '  #3 #3 /"  = 1 $2 + ##66 * #'  = $#7 #6' = 8#  = $#2' = 49 0"  = 1 $2+##*# '  ## ## "  / = 1 $2 +99 *# '  / = $#:9 ' = 73 ' 13* + ,1 +  / #  1-

0adi terdapat 12 solusi dari persamaan

>?@ 2    3 .

 +  +  = 6: dengan  ; 6