The set A- B C C - B- C is equal to

The correct option is D A ^ C ∪ B Let S=(A∩ #160; B^C)^C∪ (B ∩ C) ⇒ S = (A^C∪ #160; B)∪ (B ∩ C) De Morgan's Law ⇒ S = A^C∪ #160; (B∪ ...

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The set A∩ ...

Question

The set ${(A \cap B^{C})}^{C} \cup (B \cap C)$ is equal to

A^{C} \cup B \cup C

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A^{C} \cup B

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A^{C} \cup C^{C}

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A \cup B

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Solution

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A, B, C

A^{C} \cap B \cap C^{C} =

∣ ∣ ∣ ∣ \begin{matrix} 1 & 1 & 1 b + c & c + a & a + b b + c - a & c + a - b & a + b - c \end{matrix} ∣ ∣ ∣ ∣

a - b + a b, b + c - b c

c - a - a c

2 c + a b - a c - b c

2 c - a b - a c - b c

2 c + a b + a c + b c

2 c - a b + a c + b c

|\begin{matrix} a & b - c & c - b \\ a - c & b & c - a \\ a - b & b - a & c \end{matrix}| = (a + b - c) (b + c - a) (c + a - b)

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