Using the Principle of Inclusion-Exclusion, calculate the number of elements in the union of three sets A, B, and C, given n(A)=25, n(B)=30, n(C)=20, n(A intersect B)=10, n(B intersect C)=8, n(A inter

13. D. 60 Step 1: Apply the Principle of Inclusion-Exclusion for three sets. The formula for the union of three sets A, B, and C is: n(A ∪ B ∪ C) = n(A) + n(B) + n(C) − n(A ∩ B) − n(B ∩ C) − n(A ∩ C) + n(A ∩ B ∩ C) Step 2: Substitute the given values into the formula. Given: n(A) = 25, n(B) = 30, n(C) = 20, $n(A ∩ B

Using the Principle of Inclusion-Exclusion, calculate the number of elements in the union of three sets A, B, and C, given n(A)=25, n(B)=30, n(C)=20, n(A intersect B)=10, n(B intersect C)=8, n(A inter

13. D. 60 Step 1: Apply the Principle of Inclusion-Exclusion for three sets. The formula for the union of three sets A, B, and C is: n(A ∪ B ∪ C) = n(A) + n(B) + n(C) − n(A ∩ B) − n(B ∩ C) − n(A ∩ C) + n(A ∩ B ∩ C) Step 2: Substitute the given values into the formula. Given: n(A) = 25, n(B) = 30, n(C) = 20, $n(A ∩ B

Solved: Using the Principle of Inclusion-Exclusion…

The formula for the union of three sets $A$ , $B$ , and $C$ is:

n(A \cup B \cup C) = n(A) + n(B) + n(C) - n(A \cap B) - n(B \cap C) - n(A \cap C) + n(A \cap B \cap C)

Using the Principle of Inclusion-Exclusion, calculate the number of elements in the union of three sets A, B, and C, given n(A)=25, n(B)=30, n(C)=20, n(A intersect B)=10, n(B intersect C)=8, n(A inter

Step-by-step solution

Apply the Principle of Inclusion-Exclusion for three sets.

Substitute the given values into the formula.

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