Answer:
The empty set 
Step-by-step explanation:
Roster method is simply listing explicitly all the elements in the set, one by one (writing them between two curly brackets, and separating them through commas).
We want then to list explicitly all the elements in the following set:
The set of natural numbers x that satisfy x+2=1.
So, first we have to figure out which numbers are in that set. The set is made ONLY of those natural numbers x, that when you add 2 to them, you get 1. Clearly no natural number has that property (since the only number that would give us 1 when adding 2 to it, is the number -1, which is NOT a natural number). So there aren't any numbers at all in that set. So if we were to list them, we'd just list nothing inside the set:
(which is just the empty set)
Answer:
Positive numbers.
Step-by-step explanation:
Numbers after zero are positive numbers, which can be any number (whole or decimal/fraction). But numbers before zero are negative numbers which can be also whole or decimal fraction.
Example for numbers to the right of 0: 7, 6.5, 8/10
Answer:
Lets say that P(n) is true if n is a prime or a product of prime numbers. We want to show that P(n) is true for all n > 1.
The base case is n=2. P(2) is true because 2 is prime.
Now lets use the inductive hypothesis. Lets take a number n > 2, and we will assume that P(k) is true for any integer k such that 1 < k < n. We want to show that P(n) is true. We may assume that n is not prime, otherwise, P(n) would be trivially true. Since n is not prime, there exist positive integers a,b greater than 1 such that a*b = n. Note that 1 < a < n and 1 < b < n, thus P(a) and P(b) are true. Therefore there exists primes p1, ...., pj and pj+1, ..., pl such that
p1*p2*...*pj = a
pj+1*pj+2*...*pl = b
As a result
n = a*b = (p1*......*pj)*(pj+1*....*pl) = p1*....*pj*....pl
Since we could write n as a product of primes, then P(n) is also true. For strong induction, we conclude than P(n) is true for all integers greater than 1.
Answer:
kcbmq vnmw v s DVMX
Step-by-step explanation:
YES IM AM NOT GOING
