U={x | x is a whole number, x = 10} and P= {x | x is prime}. Express P in roster notation

Question

U={x | x is a whole number, x ≤ 10} and P= {x | x is prime}. Express P in roster notation

Answer 1

Macon,

 

Roster notation means you can either list every member of the set or use "..." to make it clear where the missing members fit in and the rule they follow.

 

For your problem, the universal set U is defined as all the negative integers, zero, and the positive integers only up to and including +10.  For set P, you have to pick out the prime numbers in U.  Working from right to left, they would be: +7, +5, +3, +1, -1, -3, -5, -7, -11, -13, -17, and I could go on for awhile longer, but never finish. 

 

However, the problems are that there  is an unending, infinite set of prime integers (determined by a mathematical proof), and we have no formula or method devised to determine them beyond any point.  We keep finding ever larger ones in magnitude by using computer programs to factor integers, mostly by trying all the possibilities up to that number. Remember that a prime can only have 1 and itself as factors, and no other divisors. And the larger the number to test by this brute force method, the more computer time required to run through all the possibilities searching for factors.

 

So your set P cannot be expressed in roster form.