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3 years ago

WILL GIVE BRAINLIEST ASAP

Mathematics

1 answer:

Blababa [14]3 years ago

7 0

Answer:

Step-by-step explanation:

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Prove that H c G is a normal subgroup if and only if every left coset is a right coset, i.e., aH = Ha for all a e G

Kaylis [27]

$\Rightarrow$

Suppose first that $H\subset G$ is a normal subgroup. Then by definition we must have for all $a\in H$ , $xax^{-1} \in H$ for every $x\in G$ . Let $a\in G$ and choose $(ab)\in aH$ ( $b\in H$ ). By hypothesis we have $aba^{-1} =abbb^{-1}a^{-1}=(ab)b(ab)^{-1} \in H$ , i.e. $aba^{-1}=c$ for some $c\in H$ , thus $ab=ca \in Ha$ . So we have $aH\subset Ha$ . You can prove $Ha\subset aH$ in the same way.

$\Leftarrow$

Suppose $aH=Ha$ for all $a\in G$ . Let $h\in H$ , we have to prove $aha^{-1} \in H$ for every $a\in G$ . So, let $a\in G$ . We have that $ha^{-1} =a^{-1}h'$ for some $h'\in H$ (by the hypothesis). hence we have $aha^{-1}=h' \in H$ . Because $a$ was chosen arbitrarily we have the desired .

5 0

2 years ago

-3/8x - 11 = 4 pls HELP me im getting no where right now.

VashaNatasha [74]

-3/8x - 11 = 4
-3/8x = 15 Add 11 to both sides
x = -40 Divide both sides by -3/8

7 0

3 years ago

A vaccine has 90% probability of being effective in preventing a certain disease. the probability of getting the disease if the

IgorLugansk [536]

If 25% of the people <em>are</em> vaccinated, then 75% of the people are <em>not</em> vaccinated. Of those not vaccinated, each has a 50% chance of contracting the disease. The probability that someone is both not vaccinated and contracts the disease is (0.75)(0.5)=0.375.
The probability that someone is vaccinated and contracts the disease is (0.25)(0.1)=0.025 (it is multiplied by 0.1 because if the vaccine is 90% effective, then there is a 10% chance someone that is vaccinated can contract the disease.
Add these together for the total: 0.375+0.025=0.4
There is a 40% chance that someone chosen at random will contract the disease.

4 0

3 years ago

Please help me :(.....

monitta

Answer:

the answer is C.........

7 0

3 years ago

What is the value of the underlined digit in 207 underlined digit 7

ladessa [460]

Answer:

Its just 7

Step-by-step explanation:

Count the places. 200+7=207

3 0

3 years ago