Can anyone prove with a counterexample that IF A is a subset of B and B subset of C then A is a subset of C.?

Question

For all sets A, B, and C, Can anyone prove with a counterexample that IF A is a subset of B and B subset of C then A is a subset of C.

Answer 1

One does not prove with a counterexample, by definition a counterexample refutes or disproves a proposition or theory.

Answer 2

all individuals comprehend that a subset is defined as a team A is a subset of B if "A belongs to B" in diverse words, if A intersection B= A and A union B = B. it relatively is a obligatory and sufficient subject for a subset. enable's do this definition for NULL set... (i) NULL union A = A (ii) NULL intersection A = NULL { from the very definition of NULL, even besides the shown fact that use n(NULL)=0 and coach the above (i) and (ii) } subsequently NULL satisfies the sufficient subject for SUBSET defined above. subsequently NULL is a subset of A, for any set A.

Answer 3

The clearest way to see that the statement you are talking about is always true is by using a Venn diagram.
Venn diagrams are illustrations used in the branch of mathematics known as set theory. They show all of the possible mathematical or logical relationships between sets (groups of things).
In this case you could show the relationship between the sets using three concentric circles. A being in inner circle and C being the outer.

Counterexamples are normally used to show that a general statement is false by finding a case for which the statement is fales.

Answer 4

unfortunately, it's true... so there's no counterexample(unless you gave the wrong statement)... proof : let x in A, so x is in B since A is a subset of B... but B is a subset of C, so x is in C... so we have if x is in A, then x is in C... so A is a subset of C...