All Questions
Tagged with propositional-calculus boolean-algebra
322
questions
4
votes
1
answer
496
views
Can we convert this statement about sets into a statement of propositional logic?
A question was just asked here about proving
$$A⊆(B∪C)⟺A\setminus C⊆B.$$
We can prove this statement directly, using the concepts of first-order logic.
"Suppose $x \in A \setminus C$ and that $A⊆(...
- 68.1k
7
votes
4
answers
4k
views
proving logical equivalence $(P \leftrightarrow Q) \equiv (P \wedge Q) \vee (\neg P \wedge \neg Q)$
I am currently working through Velleman's book How To Prove It and was asked to prove the following
$(P \leftrightarrow Q) \equiv (P \wedge Q) \vee (\neg P \wedge \neg Q)$
This is my work thus far
$...
2
votes
2
answers
5k
views
How to apply De Morgan's law?
If for De Morgan's Laws
$$( xy'+yz')' = (x'+y)(y'+z)$$
Then what if I add more terms to the expression ...
$$(ab'+ac+a'c')' = (a'+b)(a'+c')(a+c)?$$
- 215
7
votes
2
answers
977
views
Which law of logical equivalence says $P\Leftrightarrow Q ≡ (P\lor Q) \Rightarrow(P\land Q)$
I'm going through the exercises in the book Discrete Mathematics with Applications. I'm asked to show that two circuits are equivalent by converting them to boolean expressions and using the laws in ...
- 71
3
votes
1
answer
470
views
Boolean Algebra Transform
I am revisiting Boolean algebra after a long while.
Can somebody help show me how to simplify the LHS to get the RHS?
$$abc * a'bc + (abc)' * (a'bc)'\quad = \quad \;b'+c'$$
- 273
2
votes
2
answers
397
views
How to prove that $(A \lor B) \land (\lnot A \lor B) = B$
I know this is fairly basic, and I understand that it becomes
$$
\begin{align}
(A \land \lnot A) \lor B \\
F \lor B \\
B
\end{align}
$$
However, I can't work out how to prove that it becomes that ...
- 269
23
votes
3
answers
130k
views
De-Morgan's theorem for 3 variables?
The most relative that I found on Google for de morgan's 3 variable was: (ABC)' = A' + B' + C'.
I didn't find the answer for my question, therefore I'll ask here:
...
- 3,470
30
votes
5
answers
99k
views
Prove XOR is commutative and associative?
Through the use of Boolean algebra, show that the XOR operator ⊕ is both commutative
and associative.
I know I can show using a truth table.
But using boolean algebra?
How do I show? I totally have no ...
- 501
2
votes
2
answers
6k
views
Simplifying the following expression using Boolean Algebra
Simplify the following expression using Boolean Algebra into sum-of-products (SOP) expressions
. refers to AND
+ refers to OR
a'.b'.c' + a.b'.c' + a.b.c'
This is what I have so far.
a'.b'.c' + a....
- 501
0
votes
2
answers
3k
views
Boolean Algebra equivalency
Which Boolean algebra laws are required to show that
$$(\lnot y \land \lnot z) \lor (x \land ((\lnot y \land z) \lor (y \land \lnot z))) = (\lnot y \land \lnot z) \lor (x\land (\lnot (y \land z)...
- 1,557
2
votes
4
answers
158
views
Proof that $B \land ( B \lor C) = B$?
In my logic design exam today I was given this question:
Show that:
$$ B \land ( B \lor C) = B $$
It's asking for a proof for this expression. Could someone please explain how such expression ...
user54251
1
vote
0
answers
737
views
Inverse function in multi-valued logic through the Webb function
Let Webb function in multi-valued logic as $Webb(x, y) = W(x, y) = Inc(Max(x, y))$. There is a theorem about any function in any multi-valued logic can be represented through the Webb function.
Then ...
- 1,211
1
vote
1
answer
592
views
Transforming statements of a query language to propositional logic
I have a custom query language which expresses containment relations between variables. Containment in this context is simply an object (A) in programming language X (java/C#/python etc: a language ...
- 113
2
votes
2
answers
4k
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Boolean Simplification: (A+C)(!A+B)(B+C) = BC
How might I solve this? I can't find any problem similar to this, and I always end up with the wrong terms.
If (AB) = 0 and (A+B) = 1, prove that (A+C)(!A+B)(B+C) = BC
- 43
-1
votes
2
answers
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Boolean Algebra - Truth Table
X'Y'Z' + XYZ
I have the equation above (Boolean Algebra truth table), and as I know, if I get x' and the value of x is 0, the value will change to 1. But Y' with the top bar being higher, what ...
