Question

A={x:2x+1,x€n,x<=5},B={x:x is a composite number,x<=12},then show that (AUB)-(A intersection B)=(A-B)U(B-A)​

Answer 1

Proof:

Step 1. Finding the sets

A = { x : 2x + 1, x ∈ lN, x ≤ 5 }

= { 3, 5, 7, 9, 11 }

B = { x : x is a composite number, x ≤ 12 }

= { 4, 6, 8, 9, 10, 12 }

A U B = { x : x ∈ A or x ∈ B }

= { 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 }

A ∩ B = { x : x ∈ A and x ∈ B }

= { 9 }

A - B = { x : x ∈ A but x ∉ B }

= { 3, 4, 5, 6, 7, 8, 10, 11, 12 }

B - A = { x : x ∈ B but x ∉ A }

= { }

Step 2. Proving the statement

L.H.S. = (A U B) - (A ∩ B)

= { x : x ∈ (A U B) but x ∉ (A ∩ B) }

= { 3, 4, 5, 6, 7, 8, 10, 11, 12 }

R.H.S. = (A - B) U (B - A)

= { x : x ∈ (A - B) or ∈ (B - A) }

= { 3, 4, 5, 6, 7, 8, 10, 11, 12 }

So L.H.S. = R.H.S.

Hence, proved.