Suppose U = {1,2,3,4,5,6,7,8}, A = {1,3,5,7}, and B = {4,5,6}. Tell whether each statement is true or false. B c= U
True
To determine whether the statement "B c= U" is true or false, we need to check if every element in set B is also an element in set U.
First, let's list the elements of set U: {1, 2, 3, 4, 5, 6, 7, 8}.
Next, let's list the elements of set B: {4, 5, 6}.
Now, we need to check if all elements in B are also in U.
Checking each element one by one:
- Is 4 in U? Yes, 4 is in U.
- Is 5 in U? Yes, 5 is in U.
- Is 6 in U? Yes, 6 is in U.
Since all the elements of B are also in U, we can say that B is a subset of U. Therefore, the statement "B c= U" is true.
The statement "B c= U" means that all elements of set B are also elements of set U. In this case, B = {4,5,6} and U = {1,2,3,4,5,6,7,8}. Let's check if all elements of B are also elements of U:
- 4 is an element of B and also an element of U.
- 5 is an element of B and also an element of U.
- 6 is an element of B and also an element of U.
Therefore, all elements of B are indeed elements of U. This means the statement "B c= U" is true.