1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
LuckyWell [14K]
3 years ago
8

Show algebraically(using laws) that: ¬(p∧q)∨ p ≡ TRUE In your answer make sure that you (1) Show your steps (2) Do not skip any

steps and (3) Justify each step with the name of the law being used.
Mathematics
1 answer:
Vladimir [108]3 years ago
5 0

We start by applying De Morgan's law:

\neg (p \wedge q) \vee p \equiv [(\neg p) \vee (\neg q)] \vee p.

We now use the fact that the disjunction is commutative:

[(\neg p) \vee (\neg q)] \vee p \equiv p \vee [(\neg p) \vee (\neg q)].

We now use the fact that the disjunction is distributive:

p \vee [(\neg p) \vee (\neg q)] \equiv [p \vee (\neg p)] \vee (\neg q).

Using the law of excluded middle, we have p \vee (\neg p) \equiv \textrm{TRUE}, so that:

[p \vee (\neg p)] \vee (\neg q) \equiv \textrm{TRUE} \vee (\neg q).

We finally use the fact that TRUE is the absorbing element of the disjunction:

\textrm{TRUE} \vee (\neg q) \equiv \textrm{TRUE}.

You might be interested in
What is the nth term rule for the sequence -5, -7 -9 -11 -13​
MrMuchimi

Answer:

an=-2n-3

Step-by-step explanation:

3 0
3 years ago
To make purple paint, you need 3 parts red and 5 parts blue. How much red paint is needed if I use 20 ounces of blue paint?
mina [271]

Answer:

12

Step-by-step explanation:

5x4=20

3x4=12

4 0
3 years ago
Read 2 more answers
Plz help will give brainliest<br><br> scientific notion
zzz [600]

Answer:

Step-by-step explanation:

3*10^10 / 6*10^10 = 0.5

The 10^10 cancel out. 3/6 = 0.5

7 0
3 years ago
What is equivalent to 2^5
Akimi4 [234]

Answer:

Step-by-step explanation:

2⁵ = 2*2*2*2*2

     = 32

3 0
3 years ago
Which shows the rational expression written using the least common denominator x 1/4x2 x 1/x2
Luba_88 [7]

The rational expression written using the least common denominator  \frac{x+1}{4x^{2} }+\frac{x+1}{x^{2} }\\ is \frac{x+1}{4x^{2} }+\frac{4(x+1)}{4x^{2} }.

<h3>What is a rational expression?</h3>

The ratio of two polynomials is displayed in rational expressions. It indicates that the denominator and numerator are polynomials. It is an algebraic expression that has a ratio and an unknown variable, just like a fraction. Although we can simplify this kind of equation with the aid of a calculator.

Because one is divided by the other, just like a ratio, it is a "rational expression."

The polynomial that we divide by cannot be zero, as a reminder.

The least common denominator for 4x^{2} and x^{2} is calculated to be 4x^{2}.

Thus, the required rational expression is \frac{x+1}{4x^{2} }+\frac{4(x+1)}{4x^{2} }<em>.</em>

Learn more about rational expressions here:

brainly.com/question/1928496

#SPJ4

4 0
2 years ago
Other questions:
  • A car travels 200 miles in the same time that a train travels 300 miles. The speed of the train is 20 miles per hour more than t
    9·1 answer
  • Given the expression 5x^2y+ 2x - 4xy^2 - 5xy + 9x^2y, select the like term that would combine with 5x^2y.
    11·1 answer
  • What is 32+56•45? Please answer!
    7·2 answers
  • to go to the dog beach, it costs $3 plus $2 per dog. write an equation that shows this situation, where "x" represents the numbe
    12·1 answer
  • For every hour that noah stufies, his test score goes up 3 points. Explain which is the independent variable and which is the de
    8·1 answer
  • last year 950 people attended a towns annual parade. this year 1520 people attended. what was the percent increase in attendance
    12·2 answers
  • Solve each linear-quadratic system algebraically. Show all work.
    6·1 answer
  • An event lasts 5 hours and 30 minutes. How long did the event last in seconds?
    14·2 answers
  • Simplify the expression and combine lime terms<br>. 2(x + 6) + 3x + 4​
    10·2 answers
  • What are the domains of this relation?
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!