Question

A = {5, 7, 9, 11, 13, 15) and B = {7, 8, 11, 15, 20} and C = {5,8,9, 11, 13, 15, 17, 20} Verify that: An (BuC) = (A n B) n C.​

Answer 1

Given three sets A, B, and C. Verify that $A\cap (B\cup C)=(A\cap B) \cap C$

Explanation:

• Let there be two sets denoted by P and Q.
• Then the operation '$\cap$' represents the intersection of both sets. That is it gives the common data values from both sets.
• Then the operation '$\cap$' represents the union of both sets. That is it gives all the values occurring at least once in both sets.  
• Now we have, $A=\{5, 7, 9, 11, 13, 15\},\ \ B=\{7, 8, 11, 15, 20\},\ \ C=\{5,8,9, 11, 13, 15, 17, 20\}$  
• Therefore on the left-hand side we have,  
• $B\cup C=\{5,7,8,9,11,13,15,17,20\}\\A\cap (B\cup C)=\{5, 7,9,11,13,15\}$     ----(a)
• Now on the right-hand side we have,
• $A\cap B=\{7,11,15\}\\(A\cap B) \cap C= \{11,15\}$                        ----(b)
• From (a) and (b) we can say that for the given sets $A\cap (B\cup C)\neq (A\cap B) \cap C$