Is this set closed under multiplication C={0,1,3} explain why or why not.
Please help ASAP!!!
Is 3x3 in the set?
To determine if a set is closed under multiplication, we need to check if the product of any two elements in the set is also in the set.
Let's consider the set C = {0, 1, 3}.
1) Multiplying 0 with any element:
- 0 * 0 = 0, which is in the set C.
- 0 * 1 = 0, which is in the set C.
- 0 * 3 = 0, which is in the set C.
2) Multiplying 1 with any element:
- 1 * 1 = 1, which is in the set C.
- 1 * 3 = 3, which is in the set C.
3) Multiplying 3 with any element:
- 3 * 3 = 9, which is NOT in the set C.
Since 9 is not an element in the set C, we can conclude that the set C = {0, 1, 3} is not closed under multiplication.
To determine if the set C={0, 1, 3} is closed under multiplication, you need to check if the product of any two numbers in the set is also in the set.
In this case, you need to multiply each number with every other number in the set and check if the result is in the set.
Let's check:
0 * 0 = 0 ∈ C
0 * 1 = 0 ∈ C
0 * 3 = 0 ∈ C
1 * 0 = 0 ∈ C
1 * 1 = 1 ∈ C
1 * 3 = 3 ∈ C
3 * 0 = 0 ∈ C
3 * 1 = 3 ∈ C
3 * 3 = 9 ∉ C
From the above calculations, we can see that all the products of numbers in the set except 3 * 3 = 9 are in the set C. Since there is one product (9) that is not in the set, C is NOT closed under multiplication.
Therefore, the set C={0, 1, 3} is not closed under multiplication.