Set theory doubt

Question

Say if A is proper subset of B i.e A⊂B then is it true - 

that B⊆A (B is subset of A)?

Also one more thing - if  A⊂B then AUB = A  where U means UNION

Answer 1

Q.  if A is proper subset of B i.e A⊂B then is it true - 

that B⊆A

Ans. No , Never since Ais proper subset hence B is Strictly greater(superset)  than A niether equal nor smaller(subset)

Q. A⊂B then AUB = A  where U means UNION

A. No ,Never as you can see a being proper subset is completely inside B so taking union that is all elements of B and A (each element taking only once) will surely give bigger part as the result here it would be B.

Comments

@G.K.T @hs_yadav As you said, Now consider this - 

From TOC, see this ques - https://gateoverflow.in/2637/gate1995_2-24 and read Arjun Sir's Answer - 

we know, RL⊂CFL, then when we do RL U CFL = RL where as we should get CFL, right?

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 @iarnav

i think these two having diff. concept....

yeh ....here u are right. ...but one point to note...

here both the set having different domains(RL and CFL)......

but in the case of mathematical set both having same rules....

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Yes, makes sense, Thanks brother!

Answer 2

here

1. A⊂B represents-> B={A+something}

2.B⊆A represents-> A={B+something or only B}

therefor if 1st is true then 2nd cann't be true.....

AND

if  A⊂B{B+something} .. then AUB != A but AUB =B.....?????

 

Set Theory Symbols- Maths Symbols with Examples | Byju's

Answer 3

No because if  A is subset of B  than it means   A is smaller than B which means AUB  will give B not A