Aside from the hydrogen that extends "forward from the page", priority 1 goes to the top left group (from the perspective of the TAS) because of the chlorine atom. Priority 2 goes to the bottom left group because of the carbon atom attached to another two carbon atoms. Priority 3 goes to the bottom right group, which has a carbon attached to only one other carbon at the point of difference with the group that has priority 2. When the hydrogen atom attached to the TAS is viewed as going back into the page, the circle created by going from priority 1 to priority 3 is clockwise, so we assign this TAS to be R. Cis and trans are irrelevant to TAS. 

The given images are Fisher projections of the molecules. To compare them, we must mentally rotate the substituents around the carbon-carbon bond through the molecule's center, as well as consider flipping the projection end-over-end.

If the molecule to the left were flipped directly end-over-end, it will match the molecule to the right, with the methyl pointed upward in the front plane and the ethyl pointed downward in the rear plane. These molecules are identical.

Carbon 1 is not a stereocenter as both constituents on the carbon are identical. For carbon 2, the bromine is the attachment with the most priority, followed by carbon 3, then carbon 1. Because bromine is in the back, the stereocenter is designated as an S. For carbon 3, the alcohol group is the attachment with the most priority, followed by carbon 2, then carbon 4. Because alcohol is in the front, the stereocenter is designated as an S.

The molecules shown contain three stereocenters as evidenced by the bonds of carbons 2, 3, and 4 to four unique groups. Rotating the molecule on the right 180 degrees in the horizontal plane reveals that only carbon 2 differs in absolute configuration (R/S). As a general rule, switching the absolute configurations of all stereocenters present in a compound yields its enantiomer. Switching the configuration at least one stereocenter, but not all, yields diastereomers, non-superimposable stereoisomers that are not mirror images. The two molecules shown are diastereomers. A molecular modeling kit can prove extremely useful in visualizing the difference in such situations.

To label each stereocenter as R or S, we must use the Cahn-Ingold-Prelog priority system.

Lets start with stereocenter 1: The  is given first priority because it is the most massive constituent. The carbon to the right is given second priority because it is closer to the alcohol group and the carbon to the left is given third priority. These atoms lay clockwise by priority. However, because the hydrogen (not depicted) is in the front, we know that the stereocenter should be labeled as S.

Stereocenter 2: The  is given first priority. The carbon on top is given second priority while the carbon on the bottom is given third priority. These atoms lay counterclockwise by priority. Because the hydrogen (not depicted) already faces toward the rear, we know that the steroecenter should be labeled as S.

To find the number of stereo isomers in a given molecule, we must count the number of stereocenters first.

 (indicated by red dots)

Then, use the formula  to get the number of stereoisomers ( being the number of stereocenters).

Corresponding stereoisomers differ in biological properties. The inversion of just one stereocenter on a large, complex molecule can alter the biological properties of the entire molecule. All other statements are true.

To find the number of diastereomers, we must first find the number of stereocenters, then the number of stereoisomers. The stereocenters are the carbon atoms with the red dots next to them, we have three:

To find the number of stereoisomers, we use the formula , where  is the number of stereocenters. We have 8 stereoisomers. Finally, the definition of a diastereomer is a stereoisomer that is not an enantiomer. Optically active molecules have only one enantiomer, so that leaves us with 7 remaining diastereomers (including the original molecule itself).

There are 4 chiral carbons on the molecule shown below:

The number of stereoisomers for a given molecule = 2ⁿ where n equals the number of chiral centers (in this case 4). Also there are no internal planes of symmetry, so there is no possibility for meso compounds.

The following products are a mix of constitutional isomers and stereoisomers.