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. A c= B
False. The statement "A c= B" means that every element in set A is also an element in set B. However, in this case, A has elements {1, 3, 5, 7} while B has elements {4, 5, 6}, and none of the elements in A are present in B. Thus, the statement is false.
The statement "A c= B" can be read as "A is a subset of B." To determine whether this statement is true or false, we need to check if all the elements of set A are also present in set B.
Let's compare the elements of A and B:
A = {1,3,5,7}
B = {4,5,6}
Looking at the elements, we see that all the elements in A are not present in B. A contains the elements 1, 3, 5, and 7, while B contains the elements 4, 5, and 6.
Therefore, the statement "A c= B" is false. A is not a subset of B because it has elements that are not present in B.
To determine whether the statement "A c= B" is true or false, we need to check if every element in set A is also an element in set B.
Step 1: Let's compare each element in set A to set B:
- The element 1 is not in set B.
- The element 3 is not in set B.
- The element 5 is in set B.
- The element 7 is not in set B.
Step 2: Since not every element in set A is also an element in set B, we can conclude that the statement "A c= B" is false.
Explanation: In set theory, "A c= B" means that set A is a subset of set B, indicating that every element in A is also an element in B. To determine if a set is a subset of another set, we compare each element in the first set to the second set. If every element in the first set is found in the second set, then the first set is considered a subset of the second set. However, if there is at least one element in the first set that is not found in the second set, then the first set is not a subset of the second set.