Question

If $A \not\subset B$ and $B \not\subset C$, then A \not\subset C[/tex]]. State whether the statement is True (or) False And Justify it

Answer 1

Let us assume that A = {1, 2, 3}
B = {2, 3, 4, 5, 6}
C = {1, 2, 3, 7, 8, 9}
here you can see that,
{1, 2, 3}$\not\subset$ {2, 3, 4, 5, 6} e.g., $A\not\subset B$.
similarly, {2, 3, 4, 5, 6} $\not\subset$ {1, 2, 3, 7, 8, 9} e.g., $B\not\subset C$

but we observed that,
{1, 2, 3}$\subset$ {1, 2, 3 ,7, 8, 9}
e.g., $A\subset C$

thus, the given statement is false