group

Question

Let S={1,2,3} and P(s) is power set of S.A binary operation  * is defined  by  A*B = (A-B) U (B-A). if (P(S),*) is a group then complement of {1} is

a){1}

b){2}

c){3}

d){2,3}

Comments

ans??

Answer 1

$P\left ( S \right )=\left \{ \Phi ,\left \{ 1 \right \},\left \{ 2 \right \},\left \{ 3 \right \},\left \{ 1,2 \right \} ,\left \{ 2,3 \right \}\left \{ 1,3 \right \},\left \{ 1,2,3 \right \}\right \}$

And A*B shows that A and B will have no common element

So, we can say complement of {1} is element which are no connection with {1}

that will be {2},{3},{2,3}

So, in one word we can say it is a combination of 2,3

D) will be answer

Comments

what is the preposition logic form of A * B as per given definition of *

is it {∀aϵA(aϵA→a∉B)} U {∀aϵB(aϵB→a∉A)}

??

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@srestha What does complement have to do with Groups?

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not related, I think

But as we are taking w.r.t binary operations A and B

So, we can think A contains complements of B