Question

The set a intersection b dash whole dash union b intersection c is equal to

Answer 1

Related Answer. For A = {1, 2, 3, 4), B = {3, 4, 5, 6} and C = { 1, 2, 6, 8), verify the distributivity of union over intersection. More Related Question & Answers. Disclaimer.

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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