For sets A, B, C is a subset of U, prove or disprove (with a counter-example) the following: If A is a subset of B, B is not a subset of C, then A is not a subset of C,
A={1,2}
B={1,2,3}
C={1,2,4}
false
To prove or disprove the statement "If A is a subset of B, B is not a subset of C, then A is not a subset of C," we can start by assuming that A is a subset of B and B is not a subset of C.
To prove that A is not a subset of C, we need to find a counterexample that shows a scenario where A is a subset of B, B is not a subset of C, but A is still a subset of C.
Here's an example that disproves the statement:
Let U be the universal set, A = {1, 2}, B = {1, 2, 3}, and C = {2, 3, 4}.
In this example, we can see that A is a subset of B since all the elements of A, namely {1, 2}, are also present in B. Additionally, we can see that B is not a subset of C since B contains the element 3, which is not present in C.
However, if we examine the elements in A and C, we see that A is still a subset of C. Both A and C share the element 2, which is present in both sets. Therefore, A is a subset of C even though B is not a subset of C.
This counterexample disproves the statement, as it shows a scenario where A is a subset of B and B is not a subset of C, but A is still a subset of C.