State the dual of each theorem in Exercise 13. (Here you will want to use the result of Example 3.19 in conjunction with Theorem 3.5.)
In Exercise 13
Consider the membership table (Table 3.7). If we are given the condition that A Š‚ B, then we need consider only those rows of the table for which this is true - rows 1, 2, and 4, as indicated by the arrows. For these rows, the columns for B and A U B are exactly the same, so this membership table shows that A Š‚ B ‡’ A U B = B.
Table 3.7

Use membership tables to verify each of the following:
a) A Š‚ B ‡’ A ˆ© B = A
b) [(A ˆ© B = A) ˆ§ (B U C = C)] ‡’ A U B U C = C
c)

d) A ˆ† B = C ‡’ A ˆ† C = B and B ˆ† C = A

1 01