Answer

Step by step solution by experts to help you in doubt clearance & scoring excellent marks in exams.

Apne doubts clear karein ab Whatsapp par bhi. Try it now.

CLICK HERE

Watch 1000+ concepts & tricky questions explained!

95.4 K+

4.8 K+

Text Solution

Solution :

(i) Statement, if `x in A and A in B` then `x in B` is false <br> Example : Let `A = {2} and B = {{2},3}` <br> It is clear that `2 in A and A in B` but `A cancel(in)B` <br> (ii) Statement, if `A sub B and B in C` then `A in C` is false. <br> Example : Let `A = {1},B={1,2} and C={1,2},3,4}` <br> It is clear that `A sub B and B in C` but `A cancel(in)C` <br> (iii) Statement, if `A sub B and B sub C`, then `A sub C` is true <br> Let `x in A` <br> `:. A sub B and x in A` then `x in B` <br> but `B sub C and x in B` then `x in C` <br> `because x in A rArr x in C` <br> `:. A sub C` <br> Therefore, if `A sub B and B sub C`, then `A sub C` <br> (iv) Statement, if `A cancel(sub)B and B cancel(sub)C`, then `A sub C` is false <br> Example : Let `A = {1,2}, B = {3,4} and C= {1,5}` then elements 1 and 2 of A are not in B from which `A cancel(sub)B` and elements 3 and 4 of B are not in C from which `B cancel(sub)C` <br> But element 2 of A is not in C from which `A cancel(sub)C` <br> (v) Statement, if `x in A and A cancel(sub)B`, then `x in B` is false <br> Example : Let `A = {1,2} and B = {2,3,4}` <br> It is clear that `1 in A and A cancel(sub)B` then `1 cancel(in)B` <br> (vi) Statement, if `A sub B and x cancel(in)B` then `x cancel(in)A` is true i.e, all elements of A are also in B <br> i.e., if any element is not in B then it will not also be in A <br> i.e., `x cancel(in)B rArr x cancel(in)A` <br> Therefore, if `A sub B and x cancel (in) B` then `x cancel(in) A` <br> Therefore, if `A sub B and x cancel (in) B` then `x cancel (in) A`.