Siena Duran

2022-02-12

Let H be a subgroup of a group G and $a,b\in G$ . Then $a\in bH$ if and only if

1)$ba-1\in H$

2)$ba\in H$

3)$b-1a\in H$

4) None of these

1)

2)

3)

4) None of these

Johnathan Carpenter

Beginner2022-02-13Added 12 answers

Given:

H be a subgroup of a group G.

i.e.$H\subseteq G$ .

and$a,b\in G$
If $a\in bH$ (1)

$b\in bH$

$\Rightarrow {b}^{1}\in bH(\therefore a\in G\Rightarrow {a}^{1}\in G)$ (2)

Now from eq-n (1) and (2)

$a\in bH\text{}\text{and}\text{}{b}^{1}\in bH$

then${b}^{1}a\in {b}^{1}\left(bH\right)$

${b}^{1}a\in \left({b}^{1}b\right)H$

${b}^{1}a\in H$

H be a subgroup of a group G.

i.e.

and

Now from eq-n (1) and (2)

then