▁P ( n ) ▁is ▁the ▁predicate ▁" 2 · n ▁> ▁ 2 ▁+ ▁n " ▁and ▁N ▁is ▁the ▁set ▁of ▁natural ▁numbers , ▁then : ▁▁▁ ▁is ▁the ▁( false ) ▁statement : ▁For ▁all ▁natural ▁numbers ▁n , ▁ 2 · n ▁> ▁ 2 ▁+ ▁n . ▁ ▁Similarly , ▁if ▁Q ( n ) ▁is ▁the ▁predicate ▁" n ▁is ▁composite ", ▁then ▁▁▁ ▁is ▁the ▁( true ) ▁statement : ▁For ▁all ▁natural ▁numbers ▁n , ▁if ▁n ▁is ▁composite , ▁then ▁ 2 · n ▁> ▁ 2 ▁+ ▁n ▁ ▁and ▁since ▁" n ▁is ▁composite " ▁implies ▁that ▁n ▁must ▁already ▁be ▁a ▁natural ▁number , ▁we ▁can ▁short en ▁this ▁statement ▁to ▁the ▁equivalent : ▁▁▁ ▁For ▁all ▁composite ▁numbers ▁n , ▁ 2 · n ▁> ▁ 2 ▁+ ▁n . ▁ ▁Several ▁variations ▁in ▁the ▁notation ▁for ▁quant ification ▁( which ▁apply ▁to ▁all ▁forms ) ▁can ▁be ▁found ▁in ▁the ▁quant ification ▁article . ▁There ▁is ▁a ▁special ▁notation ▁used ▁only ▁for ▁universal ▁quant ification , ▁which ▁is ▁given : ▁▁▁ ▁The ▁parentheses ▁indicate ▁universal ▁quant ification ▁by ▁default . ▁ ▁Properties ▁ ▁Neg ation ▁ ▁Note ▁that ▁a ▁quant ified ▁propos itional ▁function ▁is ▁a ▁statement ; ▁thus , ▁like ▁statements , ▁quant ified ▁functions ▁can ▁be ▁neg ated . ▁The ▁notation ▁most ▁mathemat icians ▁and ▁log icians ▁util ize ▁to ▁denote ▁neg ation ▁is : ▁. ▁However , ▁some ▁use ▁the ▁til de ▁( ~ ). ▁