Verify that if H = (x, x) : x E lR}, then H is a subgroup of lR x lR (with + as the operationin each component). Describe the right cosets of H in lR x lR geometrically. (H is called thediagonal subgroup of lR x lR. See 15.28.)

CHAPTER 13 Activity PREGNANCY AND BREASTFEEDING – CASE STUDY Lisa and her husband have decided that they are ready to prepare for their first child. Lisa is 26 years old, weighs 125 pounds and is 5’6”. Lisa has been reading everything she can find on pregnancy because she knows that her prepregnancy health is important to the success of her pregnancy. She knows she should avoid alcohol, especially because alcohol is potentially toxic to the growing fetus in the first weeks of pregnancy, and she could become pregnant and not know about it right away. Lisa is not a smoker and does not take any medications. Although, she does drink 4 cups of coffee per day and drinks 3 diet cokes each day. She has already modified her diet to include