Question

State whether the given statement is true or false :
(i) if `A sub B and x lin ` then x lin A`.
(ii) If `A sube phi` then A = phi `
(iii) If `A,B and C` are three sets such that ` in 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, B and C are three sets such taht ` A cancel(sub) B and B cancel(sub)C` " then " A cancel(sub)C`.
(vi) If A, B are sets such that ` x in A and A in B` then `x in B`.

Answer 1

Correct Answer - (i) True
(ii) True
(iii) False
(iv) False
(v) False
(vi) False
(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`.