Over the universe of positive integers,define p(n): n is prime and n < 32.q(n): n is a power of 3.r(n): n is a divisor of 27.Please explain if possible, Thanks!
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Answer and explanation:Over the universe of positive integers, define the following.The universe of discourse is [tex]U=Z^+[/tex] i.e. set of positive integer.[tex]U=Z^+=\{1,2,3,4,5.....\}[/tex]a) p(n) : n is prime and n < 32.The set form in which all numbers are prime and less than 32.So, [tex]p(n)=\{1,3,5,7,11,13,17,19,23,29,31\}\in Z^+[/tex]b) q(n): n is a power of 3.The set form in which all numbers which has power of 3.So, [tex]q(n)=\{3^0,3^1,3^2,3^3,3^4...\}\in Z^+[/tex][tex]q(n)=\{1,3,9,27,81...\}\in Z^+[/tex]c) r(n): n is a divisor of 27.The set form in which all numbers which is factor of 27So, [tex]r(n)=\{1,3,9,27\}\in Z^+[/tex]