Determine if the following statements are true or false. If false, explain. 

(a) In a paired analysis we first take the difference of each pair of observations, and then we do inference on these differences. 

(b) Two data sets of different sizes cannot be analyzed as paired data. 

(c) Consider two sets of data that are paired with each other. Each observation in one data set has a natural correspondence with exactly one observation from the other data set. 

(d) Consider two sets of data that are paired with each other. Each observation in one data set is subtracted from the average of the other data set's observations.