suppose you had a very small set of numbers that contained only 0 and 1 would this set be closed under addition? if not give a counterexample.
please help me
no
1+1 = 2 , which is not in the set of {0,1}
suppose you had a very small set of numbers that contained only 0 and 1 would this set be closed under addition? if not give a counterexample.
To determine if a set is closed under addition, we need to check if the sum of any two numbers from the set is still within the set.
In this case, the set only contains the numbers 0 and 1. Let's check all possible combinations:
0 + 0 = 0 (still in the set)
0 + 1 = 1 (still in the set)
1 + 0 = 1 (still in the set)
1 + 1 = 2 (not in the set)
From the above calculations, we can see that the sum of 1 and 1 is not in the set, which means the set of numbers containing only 0 and 1 is not closed under addition.
Therefore, a counterexample is 1 + 1 = 2, which is not in the set.
To determine if a set is closed under addition, we need to check if the sum of any two numbers in the set is also in the set. In your case, the set contains only 0 and 1.
Let's check all the possible combinations of adding two numbers from the set (0 and 1):
0 + 0 = 0
0 + 1 = 1
1 + 0 = 1
1 + 1 = 2
As we can see, the result of adding two numbers from the set can be 0, 1, or 2. Since 2 is not in the set, we can conclude that the set {0, 1} is not closed under addition.
A counterexample would be the sum of 1 and 1, which gives 2, which is outside the set. Therefore, we can say that the set {0, 1} is not closed under addition.