Show that the following preferences are not consistent for a rational individual

i. An individual when confronted with prices of p1 = $4 and p2 = $8 chooses q1 = 1
and q2 = 5.
ii. The same individual facing prices of p1 = $6 and p2 = $9 chooses q1 = 5 and q2 = 3.

The first income level was 4 + 40 = 44. The second income was 30 + 27 = 57. However, at the old prices he could have consumed (5,3 ) and paid only 21, so this indicates that he prefers the first bundle. However, he could have consumed the old bundle at the new prices and paid only 20 + 24 =54, which indicates he prefers the second bundle. Thus a contradiction and his preferences are not consistent