State whether the given statement is true or false : (i) if A sub B andx linthen x lin A. (ii) If A sube phi then A = phi (iii) If A,B and C are three sets such thatin B and B sub C then A sub C . (iv) If A, B and C are three sets such that A sub B and B in C " then "A in C. (v) If A, Band C are three sets such tahtA cancel(sub) B and B cancel(sub)C " then " A cancel(sub)C. (vi) If A, B are sets such thatx in A and A in B then x in B.

State whether the given statement is true or false : (i) if A sub B a

1.	State whether the given statement is true or false : (i) if A sub B andx linthen x lin A. (ii) If A sube phi then A = phi (iii) If A,B and C are three sets such thatin B and B sub C then A sub C . (iv) If A, B and C are three sets such that A sub B and B in C " then "A in C. (v) If A, Band C are three sets such tahtA cancel(sub) B and B cancel(sub)C " then " A cancel(sub)C. (vi) If A, B are sets such thatx in A and A in B then x in B.
Answer» Solution :(iii) LET `A = {a}, B = {{a, b}` and C = {{1}, b, c}. Then , `{a} in B` and `B SUB C`. But., `{a} CANCEL(sub) C`. (iv) Let A = {a}, B = {a, b} and C = {{a, b}, c}. Then, `A cancel(sub) B` and `B in C`.But, `A cancel(in)C`. Let A= {a}, B = {b,c} and C = {a, c}. Then, `A cancel(sub)B` and `B cancel(sub)C`. But `A sub C`. Let A= {x}, B = {{x}, y}. Then, `x in A` and `A in B`. But, `x in b`.