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Question Number 113801 by Study last updated on 15/Sep/20
what is the number that is evenly   divisible by 3 and 6 and but not divisible  by 2?
$${what}\:{is}\:{the}\:{number}\:{that}\:{is}\:{evenly}\: \\ $$$${divisible}\:{by}\:\mathrm{3}\:{and}\:\mathrm{6}\:{and}\:{but}\:{not}\:{divisible} \\ $$$${by}\:\mathrm{2}? \\ $$
Commented by MJS_new last updated on 15/Sep/20
6∣x ⇒ 3∣x ∧ 2∣x  3∣x ∧ 2∤x ⇒ 6∤x
$$\mathrm{6}\mid{x}\:\Rightarrow\:\mathrm{3}\mid{x}\:\wedge\:\mathrm{2}\mid{x} \\ $$$$\mathrm{3}\mid{x}\:\wedge\:\mathrm{2}\nmid{x}\:\Rightarrow\:\mathrm{6}\nmid{x} \\ $$
Commented by Study last updated on 15/Sep/20
what means it?
$${what}\:{means}\:{it}? \\ $$
Commented by JDamian last updated on 15/Sep/20
if the number is divisible by 6, then it is  divisible by 2(even).  You are asking for a number divisible by 6  and not even. You′ll find none.
$${if}\:{the}\:{number}\:{is}\:{divisible}\:{by}\:\mathrm{6},\:{then}\:{it}\:{is} \\ $$$${divisible}\:{by}\:\mathrm{2}\left({even}\right). \\ $$$${You}\:{are}\:{asking}\:{for}\:{a}\:{number}\:{divisible}\:{by}\:\mathrm{6} \\ $$$${and}\:{not}\:{even}.\:{You}'{ll}\:{find}\:{none}. \\ $$$$ \\ $$

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