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Question Number 65423 by byaw last updated on 29/Jul/19
Commented by mr W last updated on 29/Jul/19
$${all}\:{primes}\:{are}\:{not}\:{divisible} \\ $$$${by}\:\mathrm{3}\:{and}\:\mathrm{5}. \\ $$
Answered by mr W last updated on 29/Jul/19
$${from}\:\mathrm{1}\:{to}\:\mathrm{30}\:{there}\:{are}\:\mathrm{10}\:{primes}.\:{they} \\ $$$${are}\:{all}\:{not}\:{divisible}\:{by}\:\mathrm{3}\:{and}\:\mathrm{5}. \\ $$$${p}=\frac{\mathrm{10}}{\mathrm{30}}=\frac{\mathrm{1}}{\mathrm{3}} \\ $$
Commented by Rasheed.Sindhi last updated on 30/Jul/19
$${Sir},\:{I}\:{think}\:{that}\:{there}\:{are}\:\mathrm{8}\:{such}\:{primes} \\ $$$$\left({Excluding}\:\mathrm{3}\:{and}\:\mathrm{5}\:{because}\:{they}\:{are}\right. \\ $$$$\left.{divisible}\:{by}\:\mathrm{3}\:{and}\:\mathrm{5}\:{respectly}\right) \\ $$$$\:\mathrm{2},\mathrm{7},\mathrm{11},\mathrm{13},\mathrm{17},\mathrm{19},\mathrm{23},\mathrm{29}. \\ $$
Commented by MJS last updated on 30/Jul/19
![mathematical language has to be accurate “3 and 5” ≠ “3 or 5” ≠ “3 xor 5” x divisible by 3 and 5 ⇒ x=15n x divisible by 3 or 5 ⇒ x=3n or x=5n or x=15n x divisible by 3 xor 5 ⇒ (x=3n or x=5n) and x≠15n [n, k ∈Z]](Q65448.png)
$$\mathrm{mathematical}\:\mathrm{language}\:\mathrm{has}\:\mathrm{to}\:\mathrm{be}\:\mathrm{accurate} \\ $$$$``\mathrm{3}\:\mathrm{and}\:\mathrm{5}''\:\neq\:``\mathrm{3}\:\mathrm{or}\:\mathrm{5}''\:\neq\:``\mathrm{3}\:\mathrm{xor}\:\mathrm{5}'' \\ $$$${x}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{3}\:\mathrm{and}\:\mathrm{5}\:\Rightarrow\:{x}=\mathrm{15}{n} \\ $$$${x}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{3}\:\mathrm{or}\:\mathrm{5}\:\Rightarrow\:{x}=\mathrm{3}{n}\:\mathrm{or}\:{x}=\mathrm{5}{n}\:\mathrm{or}\:{x}=\mathrm{15}{n} \\ $$$${x}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{3}\:\mathrm{xor}\:\mathrm{5}\:\Rightarrow\:\left({x}=\mathrm{3}{n}\:\mathrm{or}\:{x}=\mathrm{5}{n}\right)\:\mathrm{and}\:{x}\neq\mathrm{15}{n} \\ $$$$\left[{n},\:{k}\:\in\mathbb{Z}\right] \\ $$
Commented by Rasheed.Sindhi last updated on 30/Jul/19
$${You}'{re}\:{very}\:{right}\:{sir}.{I}\:{didn}'{t}\:{care}\:{of}\:\:{that}! \\ $$
Commented by mr W last updated on 30/Jul/19
$${i}\:{agree}\:{with}\:{MJS}\:{sir}. \\ $$$${what}\:{Rasheed}\:{sir}\:{means}\:{is}\:{probably} \\ $$$${what}\:{the}\:{question}\:{really}\:{means},\:{but} \\ $$$${the}\:{question}\:{uses}\:{an}\:{inaccurate} \\ $$$${language}. \\ $$