Consider the membership table (Table 3.7). If we are given the condition that A B, then we need consider only those rows of the table

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