Question

# show step by step simplification: $¬𝑑∨((¬b∧c$∨$b∧¬c$))∧$(𝑎 ∧ 𝑏$ ∨ $¬𝑎 ∧ ¬𝑏$)∧$¬𝑐∨((¬𝑑∧𝑎$∨$𝑑∧¬𝑎$))

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## Answer to a math question show step by step simplification: $¬𝑑∨((¬b∧c$∨$b∧¬c$))∧$(𝑎 ∧ 𝑏$ ∨ $¬𝑎 ∧ ¬𝑏$)∧$¬𝑐∨((¬𝑑∧𝑎$∨$𝑑∧¬𝑎$))

Miles
4.9
To simplify the given expression, we can start by using the distributive law.

Step 1: Distribute the negation $¬$ in the first part of the expression:
¬$d∨((¬b∧c$∨$b∧¬c$))

Step 2: Distribute the negation $¬$ further inside the first part:
¬$d∨(¬b∧c$) ∧ ¬$d∨(b∧¬c$)

Step 3: Apply De Morgan's laws and distribute the ∧ $logical AND$ inside the first part:
$¬d∧(¬¬b∨¬c$) ∧ $¬d∧(¬b∨¬¬c$)

Step 4: Simplify the double negations $¬¬$:
$¬d∧(b∨¬c$) ∧ $¬d∧(¬b∨c$)

Step 5: Apply the distributive law again to the second part of the expression:
$(¬d∧b$∨$¬d∧¬c$) ∧ $(¬d∧¬b$∨$¬d∧c$)

Step 6: Simplify the expressions with ∧ $logical AND$:
$(-d∧b$∨$-d∧¬c$) ∧ $(-d∧¬b$∨$-d∧c$)

Step 7: Apply the distributive law once more:
$-d∧(b∨¬c$)∨$-d∧(¬b∨c$)

Step 8: Simplify the expressions with ∨ $logical OR$:
$-d∧(b∨¬c$)∨$-d∧(¬b∨c$)

Step 9: Apply the distributive law to the ∨ $logical OR$ outside the parentheses:
$-d∧b$ ∨ ¬c ∨ $-d∧¬b$ ∨ c

Step 10: Simplify the expressions with ∨ $logical OR$ and ∧ $logical AND$:
$(-d∧b$ ∨ $-d∧¬b$) ∨ ¬c ∨ c

Step 11: Simplify the expressions with ∧ $logical AND$:
-d ∨ ¬c ∨ c

Step 12: Simplify the expressions with ∨ $logical OR$:
-d ∨ 1

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