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High School Mathematics
Prove The Given Statements

If m = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, A = {1, 3, 5, 7}, B = {2, 4, 6, 8} and C = {3, 6, 9}, then check the following statements. And also illustrate the statements in Venn diagrams.

1. A A = A.

2. A A = A.

3. A j = j.

4. A m = A.

5. A j = A.

6. A m = m.

7. A B = B A.

8. A B = B A.

De Morgan's Laws.

1. A (B C) = (A B) (A C).

2. A (B C) = (A B) (A C)