Question

Illustrate the other De Morgan's law by selecting the region(s) corresponding to (A ∩ B)c on one copy of the diagram and Ac ∪ Bc on the other.

Option 1: Shaded region corresponding to (A ∩ B)c
Option 2: Shaded region corresponding to Ac ∪ Bc
Option 3: Both Option 1 and Option 2
Option 4: None of the above

Answer 1

De Morgan's law states that the complement of the intersection of two sets is equal to the union of their complements. To illustrate this law, you can use a Venn diagram to shade the regions corresponding to (A ∩ B)c and Ac ∪ Bc, and then compare the shaded regions.

Step-by-step explanation:

De Morgan's law states that the complement of the intersection of two sets is equal to the union of their complements. In symbols, (A ∩ B)c = Ac ∪ Bc. To illustrate this law using a Venn diagram:

• Draw two overlapping circles to represent sets A and B.
• Shade the region that corresponds to (A ∩ B)c, which means all the elements that are outside the intersection of A and B.
• On a separate copy of the diagram, shade the region that corresponds to Ac ∪ Bc, which means all the elements that are in the complement of both A and B.
• Now, compare the shaded regions on both diagrams. If they are the same, then the answer would be Option 3: Both Option 1 and Option 2. If they are different, the answer would be Option 4: None of the above.