Question

The set (aub')'u(bnc) is equal to

Answer 1

Correct Question:-

The set $\large\rm { (A \cap B')' \cup ( B \cap C) }$ is equal to?

Answer:- $\large\rm { (A \cap B')' \cup ( B \cap C)}$

$\large\rm { = ( A \cap \bar{B} ) \cup ( B \cap C)}$

$\large\rm { = ( \bar{A} \cap B) \cup ( B \cap C)}$

$\large\rm { = \bar{A} \cup B \cup C}$

$\large\rm { = A' \cup B \cup C}$

Answer 2

SOLUTION

CORRECT QUESTION

TO DETERMINE

$\sf (A \cap \: B')' \cup (B \cap C)$

EVALUATION

Here the given expression is

$\sf (A \cap \: B')' \cup (B \cap C)$

We simplify it as below

$\sf (A \cap \: B')' \cup (B \cap C)$

$\sf = \bigg[ A' \cup \: (B')' \bigg] \cup (B \cap C) \: \: \bigg( \red{De \: Morgan \: Law} \: \bigg)$

$\sf = (A' \cup \: B )\cup (B \cap C)$

$\sf = (A' \cup \: B )\cup X \: \: \bigg[ \: Let \: X = (B \cap C) \bigg]$

$\sf = A' \cup( \: B \cup X )$

$\sf = A' \cup \bigg[ B \cup(B \cap C) \bigg]$

$\sf = A' \cup B$

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