Question

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

209

likes
1046 views

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

Expert avatar
Miles
4.9
77 Answers
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

Answer:
-d ∨ 1

Frequently asked questions (FAQs)
Math question: In a right triangle, if one angle measures 30 degrees and the hypotenuse is 10 units long, what is the length of the opposite side?
+
What is the derivative of f(x) = 3x^2 + 2x + 5?
+
Find the equation of an ellipse with the center at (2, -3), major axis length 8, and minor axis length 6.
+
New questions in Mathematics
1 + 1
A college believes that 22% of applicants to that school have parents who have remarried. How large a sample is needed to estimate the true proportion of students who have parents who have remarried to within 5 percentage points?
a) A tap can supply eight gallons of gasoline daily to each of its 250 customers for 60 days. By how many gallons should each customer's daily supply be reduced so that it can supply 50 more customers for twenty more days?
a bank finds that the balances in its savings accounts are normally distributed with a mean of $500 and a standard deviation off of $40. What is the probability that a randomly selected account has a balance of more than $400?
A consulting company charges a fee of $50 per hour for consulting. If their monthly fixed costs are $1,000 and they want to make a monthly profit of $2,500, how many consulting hours should they bill per month?
(6.2x10^3)(3x10^-6)
x/20*100
7273736363-8
A force of 750 pounds compresses a spring 3 inches from its natural length, which is 15 inches. What will be the work done to compress it 3 inches more?
Substitute a=2 and b=-3 and c=-4 to evaluate 2ac/(-2b^2-a)
1. A pediatric client is prescribed digoxin for congestive heart failure. The dose prescribed is 40 mcg/kg twice daily. The child weighs 33 pounds. What is the dosage in mg to be given per dose? Round to the nearest hundredth. Calculate your answer in mg per dose. Enter numerical value only.____mg
prove that for sets SS, AA, BB, and CC, where AA, BB, and CC are subsets of SS, the following equality holds: (A−B)−C=(A−C)−(B−C)
How do you convert a fraction to a decimal
answer this math question The scale on a map is drawn so that 5.5 inches corresponds to an actual distance of 225 miles. If two cities are 12.75 inches apart on the map, how many miles apart are they? (Round to the nearest tenth) miles apart. The two cities are how many miles apart
Find the orthogonal projection of a point A = (1, 2, -1) onto a line passing through the points Pi = (0, 1, 1) and P2 = (1, 2, 3).
8(x+4) -4=4x-1
Two trains leave stations 294 miles apart at the same time and travel toward each other. One train travels at 95 miles per hour while the other travels at 115 miles per hourHow long will it take for the two trains to meet?
If the area of a circle is 75.7ft2, what is the radius? Give the answer in metres. Round answer to 2 decimal places and enter the units.
x(squared) -8x=0
The domain of the function f(x)=x+7x2−144 is (−∞,), ( ,), and ( , ∞).