Question

Let A = {a, b, c}, B = {b, d, e} and C = {e, f, g}, verify that (A Ո B) Ո C = A Ո (B Ո C)​

Answer 1

Please find below solution

Answer 2

Given :-

• Let A = {a, b, c}, B = {b, d, e} and C = {e, f, g}

To find :-

• Verify that (A Ո B) Ո C = A Ո (B Ո C)

Solution :-

• Union of sets

→ The union of A and B is the set of all those element which belong either A or to B or to both A and B is known as union of sets

→ It is denoted by " A U B " (read as A union B)

• Intersection of sets

→ The intersections of A and B is a set of all those elements that belongs to both A and B is known as intersection of sets

→ It is denoted by " A Ո B " (read as A intersection B)

It is given that

• A = {a, b, c}

• B = {b, d, e}

• C = {e, f, g}

→ (A Ո B) Ո C = A Ո (B Ո C)

• LHS = (A Ո B) Ո C

→ (A Ո B) = {b} ( " b " is common in both A and B set)

→ C = {e, f, g}

→ (A Ո B) Ո C = { } -----(i)

• No element is common. It is known as empty, null or void set

• RHS = A Ո (B Ո C)

→ (B Ո C) = {e} ( " e " is common in B and C set}

→ A = {a, b, c}

→ A Ո (B Ո C) = { } -----(ii)

• Note : No element is common. It is known as empty, null or void set}

Hence,

• From (i) and (ii)
• LHS = RHS Verified
• (A Ո B) Ո C = A Ո (B Ո C)