Question

let A={b,d,e,g,h} and B={a,e,c,h}
verify that n(A-B)=n(A)-n(AnB)​

Answer 1

• n(A - B) = 3 , n(A) = 5 , n(A ∩ B) = 2

• n(A - B) = n(A) - n(A ∩ B) is verified

Given :

A = {b,d,e,g,h} and B = {a,e,c,h}

To find :

To verify n(A - B) = n(A) - n(A ∩ B)

Solution :

Step 1 of 2 :

Find n(A - B) , n(A) , n(A ∩ B)

Here the given sets are

A = {b,d,e,g,h} and B = {a,e,c,h}

∴ n(A) = 5

A - B

= { x : x ∈ A ∧ x ∉ B }

= {b, d, g}

∴ n(A - B) = 3

A ∩ B

= { x : x ∈ A ∧ x ∈ B }

= {e,h}

∴ n(A ∩ B) = 2

Step 2 of 2 :

Verify n(A - B) = n(A) - n(A ∩ B)

LHS = n(A - B) = 3

RHS = n(A) - n(A ∩ B) = 5 - 2 = 3

∴ LHS = RHS

Hence verified

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