▁" there ▁exists ▁a ▁person ▁who ▁is ▁not ▁married " ): ▁ ▁Other ▁connect ives ▁ ▁The ▁universal ▁( and ▁exist ential ) ▁quant ifier ▁moves ▁un changed ▁across ▁the ▁logical ▁connect ives ▁ ∧ , ▁ ∨ , ▁→ , ▁and ▁ <0xE2> <0x86> <0x9A> , ▁as ▁long ▁as ▁the ▁other ▁oper and ▁is ▁not ▁affected ; ▁that ▁is : ▁ ▁Con vers ely , ▁for ▁the ▁logical ▁connect ives ▁ ↑ , ▁ ↓ , ▁ <0xE2> <0x86> <0x9B> , ▁and ▁ ← , ▁the ▁quant ifiers ▁f lip : ▁ ▁R ules ▁of ▁inference ▁▁ ▁A ▁rule ▁of ▁inference ▁is ▁a ▁rule ▁just ifying ▁a ▁logical ▁step ▁from ▁hypothesis ▁to ▁conclusion . ▁ ▁There ▁are ▁several ▁rules ▁of ▁inference ▁which ▁util ize ▁the ▁universal ▁quant ifier . ▁ ▁Universal ▁instanti ation ▁con cludes ▁that , ▁if ▁the ▁propos itional ▁function ▁is ▁known ▁to ▁be ▁univers ally ▁true , ▁then ▁it ▁must ▁be ▁true ▁for ▁any ▁arbitrary ▁element ▁of ▁the ▁universe ▁of ▁disc ourse . ▁ ▁Symbol ically , ▁this ▁is ▁represented ▁as ▁ ▁where ▁c ▁is ▁a ▁completely ▁arbitrary ▁element ▁of ▁the ▁universe ▁of ▁disc ourse . ▁ ▁Universal ▁general ization ▁con cludes ▁the ▁propos itional ▁function ▁must ▁be ▁univers ally ▁true ▁if ▁it ▁is ▁true ▁for ▁any ▁arbitrary ▁element ▁of ▁the ▁universe ▁of ▁disc ourse . ▁ ▁Symbol ically , ▁for ▁an ▁arbitrary ▁c , ▁ ▁The ▁element   c ▁must ▁be ▁completely ▁arbitrary ; ▁else , ▁the ▁logic ▁does ▁not ▁follow : ▁if ▁c ▁is ▁not ▁arbitrary ,