A = {1,2,3,9} B = <1,2, 3, 5, 6, 8, 9; and C = 14, 5, 6, 8;. All the statements about
these sets are correct except one. Select the statement that is not true.
The statement that is not true is: "Set A is a subset of set B." This is not true because set A is not a subset of set B as it does not contain all the elements of set B.
To determine which statement is not true, let's analyze each statement:
1. A is a subset of B.
2. C is a proper subset of B.
3. A ∩ C = ∅ (A intersection C is empty).
4. B ∩ C ≠ ∅ (B intersection C is not empty).
Let's evaluate each of these statements:
1. A is a subset of B: A = {1, 2, 3, 9} and B = {1, 2, 3, 5, 6, 8, 9}. Since all the elements of A are also present in B, this statement is correct.
2. C is a proper subset of B: C = {14, 5, 6, 8} and B = {1, 2, 3, 5, 6, 8, 9}. Since C contains only a subset of the elements in B, and it is not equal to B, this statement is correct.
3. A ∩ C = ∅: The intersection of A and C is empty. From the given values, A ∩ C = {}. This statement is correct.
4. B ∩ C ≠ ∅: The intersection of B and C is not empty. B ∩ C = {5, 6, 8}. This statement is correct.
Therefore, all the statements about the sets A, B, and C are true. There is no statement that is not true.