What is the simplified form of (p ∧ q) ↓ q using basic propositional logic?

In summary, to prove the statement (p ∧ q) ↓ q ≡ ¬q using the laws of logic, we can first replace the NOR operation with its definition as the negation of a logical OR. Then, we can apply the distributive law to simplify the expression further. Finally, we can use the law of double negation to get the desired result of ¬q.
  • #1
moredumbimpossi
2
0
Please help me with this thing. I'm so frustrated I can't understand propositional logic

Demonstrate this:

(p ∧ q) ↓ q ≡ ¬q

PLEASE.
 
Physics news on Phys.org
  • #2
moredumbimpossi said:
Please help me with this thing. I'm so frustrated I can't understand propositional logic

Demonstrate this:

(p ∧ q) ↓ q ≡ ¬q

PLEASE.

Hi moredumbimpossi, welcome to MHB!

What have you tried? Where are you stuck?

Simplest method to prove something like this, is to set up a truth table.
Let's start with p=0 and q=0.
What is (p ∧ q) ↓ q = (0 ∧ 0) ↓ 0 then?
 
  • #3
I like Serena said:
Hi moredumbimpossi, welcome to MHB!

What have you tried? Where are you stuck?

Simplest method to prove something like this, is to set up a truth table.
Let's start with p=0 and q=0.
What is (p ∧ q) ↓ q = (0 ∧ 0) ↓ 0 then?

Hi., thanks for replying
This has to be reduced with the laws of logic
 
  • #4
moredumbimpossi said:
Hi., thanks for replying
This has to be reduced with the laws of logic

Oh, okay.
Let's first get to basic operations then.
In general, we have $(a ↓ b) = \lnot (a \lor b)$ don't we? It's a NOR after all.
What do we get if we replace the NOR (↓) in (p ∧ q) ↓ q by those basic operations?
 

Related to What is the simplified form of (p ∧ q) ↓ q using basic propositional logic?

1. What is Propositional Logic with NOR?

Propositional Logic with NOR is a type of formal logic that uses the logical connective NOR (not or) as its main operator. It is a way of representing and analyzing logical statements and arguments using symbols and rules.

2. How does Propositional Logic with NOR differ from other types of logic?

Propositional Logic with NOR differs from other types of logic in that it uses the NOR operator as its main connective, whereas other types of logic may use operators such as AND, OR, and NOT. Additionally, Propositional Logic with NOR is a type of propositional logic, which deals with statements rather than the truth values of those statements.

3. What are the basic rules of Propositional Logic with NOR?

The basic rules of Propositional Logic with NOR include the NOR truth table, which shows the truth values of different combinations of statements connected with NOR, and the De Morgan's laws, which state that the negation of a statement connected with NOR is equivalent to the conjunction of the negations of the individual statements.

4. How is Propositional Logic with NOR used in real-world applications?

Propositional Logic with NOR is used in various real-world applications, such as in computer science and digital electronics. It is used to analyze and optimize the behavior of digital circuits, and it is also used in computer programming languages to represent logical statements and conditions.

5. What are some common misconceptions about Propositional Logic with NOR?

Some common misconceptions about Propositional Logic with NOR include thinking that it is the only type of logic, or that it is the same as Boolean logic. While it is an important type of logic, there are many other types, and Boolean logic includes other operators such as AND and OR in addition to NOR.

Similar threads

  • Set Theory, Logic, Probability, Statistics
Replies
4
Views
908
  • Set Theory, Logic, Probability, Statistics
Replies
4
Views
2K
  • Set Theory, Logic, Probability, Statistics
Replies
6
Views
2K
  • Set Theory, Logic, Probability, Statistics
Replies
8
Views
1K
  • Set Theory, Logic, Probability, Statistics
Replies
21
Views
2K
  • Set Theory, Logic, Probability, Statistics
Replies
1
Views
1K
  • Set Theory, Logic, Probability, Statistics
Replies
7
Views
1K
  • Set Theory, Logic, Probability, Statistics
Replies
4
Views
3K
  • Set Theory, Logic, Probability, Statistics
Replies
2
Views
681
  • Set Theory, Logic, Probability, Statistics
Replies
6
Views
443
Back
Top