Suppose U={1,2,3,4,5,6,7,8}, A={2,4,6}, and B={1, 2, 3}. Tell whether each statement is true or false.
A⊂U
B⊂A
every element of A is in U
3 is not in A
so, what do you think?
Uhh. Is the answer True then, False? You know what...I'll tell ya'll after I take the quick check!!
It's actually False, True.
To determine whether each statement is true or false, we can compare the elements of the sets involved.
Statement 1: A ⊂ U
To check whether set A is a subset of U, we need to verify if every element in A is also present in U.
A = {2, 4, 6}
U = {1, 2, 3, 4, 5, 6, 7, 8}
Since all the elements in set A (2, 4, and 6) are also present in set U, the statement "A ⊂ U" is true.
Statement 2: B ⊂ A
To check whether set B is a subset of A, we need to verify if every element in B is also present in A.
B = {1, 2, 3}
A = {2, 4, 6}
Not all the elements in set B are present in set A. B has the element 1, which is not in A. Therefore, the statement "B ⊂ A" is false.
To summarize:
- The statement "A ⊂ U" is true.
- The statement "B ⊂ A" is false.