Question

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

Answer 1

it is given that $x\in A$ and $A\not\subset B$

so, Let us assume that A = {1}
B = {{1}, 2, 3, 4}
here, it is clear that, 1 is the element of A. so, 1 belongs to A. but in case of B, 1 isn't elements of B. hence, 1 doesn't belongs to B.
eg., $x\in A$ and $A\not\subset B$ then, $x\notin B$

Therefore, the given statement is false.


[note :- there is little mistake in question. here you should be $x\in A$ in place of $A\in B$ ]