Question

if n( A ) =20,n( B )=28 and n (AUB) =36 then n (AnB )=?
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Answer 1

Solution:-

Given:-

=> n( A ) = 20

=> n( B ) = 28

=> n ( A ∪ B ) = 36

To find the value of

=> n( A∩B ) = ?

Now We know That

=> n( A∪B )=n( A )+n( B ) − n( A∩B )

Now Put The Value in Formula

=> 36 = 20 + 28 - n( A∩B )

=> 36 = 48 - n( A∩B )

=> 36 - 48 = - n( A∩B )

=> - 12 = - n( A∩B )

=> n( A∩B ) = 12

Answer:-

=> So Value of n( A∩B ) is 12

Some properties of sets

=>A ∩ (B ∩ C) = (A ∩ B) ∩ C. Intersection is associative.

=>A ∩ B = B ∩ A. Intersection is commutative.

=> A ∩ ∅ = ∅ = ∅ ∩ A. The empty set is the zero for intersection.

=> A ∪ (B ∪ C) = (A ∪ B) ∪ C. Union is associative.

=> A ∪ B = B ∪ A. Union is commutative.

=>A ∪ ∅ = A = ∅ ∪ A. The empty set is the identity for union.

=> A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C). Intersection distributes over union.

=> A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C). Union distributes over intersection.

=> A \ (B ∪ C) = (A \ B) ∩ (A \ C). De Morgan’s law part one.

=> A \ (B ∩ C) = (A \ B) ∪ (A \ C). De Morgan’s law part two.

=> A ∩ A = A. Intersection is idempotent.

=> A ∪ A = A. Union is idempotent.

Answer 2

Answer:

$\leadsto$$\boxed{\bold{\red{n(A∩B) = 12}}}$

Given:

• n(A) = 20

• n(B) = 28

• n(A∪B) = 36

To find:

• n(A∩B)

Formula used:

$\boxed{\bold{n(A∪B) = n(A) +n(B) -n(A∩B) }}$

Solution:

$➪$ $\sf{n(A∪B) = n(A) +n(B) -n(A∩B)}$

$➪$ $\sf{36 = 20+28 -n(A∩B)}$

$➪$ $\sf{36 = 48 -n(A∩B)}$

$➪$ $\sf{n(A∩B) = 48-36}$

$➪$ $\sf{n(A∩B) = }$$\bold{\red{12}}$