Select your path then go to Object > Path > Offset Path... and enter the amount of offset you want. The offset will enclose the path, so if it's not a closed shape, then you'll want to select the parts you want to remove and delete them. If you want to make the effect live so that you can modify the path and have the offset update, then select your path and in the Appearance panel add a new stroke at whatever weight you want, then go to Effect > Path > Offset Path... and set the offset there. The offset applied this way will also enclose your path, so if you want to delete part of it, you'll have to go to Object > Expand Appearance to make it selectable. However expanding it will also make it no longer live, so if you change the original path afterward, the offset won't update. It might work best to start your path from the center of where you want them, then keep the offsets on either side. Then select the portion you don't want and remove that, so in the end you have your set of open paths.
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