# Tagged Questions

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### How would I go from CNF to a simplified formula with less symbols?

Here's a CNF: $$(\neg A_1 \land \neg A_2 \land \neg A_3 ) \lor (A_1 \land \neg A_2 \land \neg A_3 ) \lor (\neg A_1 \land \neg A_2 \land A_3 ) \lor (\neg A_1 \land A_2 \land \neg A_3 )$$ And the ...
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### How to find a Boolean expression for a combinational logic circuit?

How to find the logic expression for a logic circuit? For example, this one. I am unsure what the circles before the gates exactly mean.
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### Show that (P→Q) ∧ (Q→R) is equivalent to (P→R) ∧ [(P↔Q) ∨ (R↔Q)]

I literally have no idea how to start this proof. I get to (P→Q) ∧ (Q→R) = (¬P ∨ Q) ∧ (¬Q ∨ R) and then I get stuck.
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### Construct XNOR with only OR gates

Is it possible to construct the XNOR gate which is given as, a XNOR b = (a AND b) OR (~a AND ~b), by using only OR gates. So from the definition, the question boils down to: can you construct the AND ...
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### Correct progression from DNF to CNF?

Trying to figure out how to transform this predicate from disjunctive normal form to conjunctive normal form (repost of an earlier question): $$( P \land Q ) \lor ( R \land S ) \lor ( P \land S )$$ ...
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### How is $((X\to Y)\to X)\to X$ a tautology?

$((X \rightarrow Y ) \rightarrow X) \rightarrow X$ converted to its disjunctive normal form is $X' + X$. Why/how does this show me why this formula a tautology?
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### Simplification of boolean algebra from “not s and p” to “not s”

I am trying to learn more about "Rules of Inference" and their application, but one thing always confuses me, and that is simplification "not s and p" to "not s". I have looked at some examples: ...
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### Is the following sentence a tautology: $(p\Rightarrow q)\vee(r \Rightarrow p)\vee(r\Rightarrow s)\vee(r\Rightarrow q)$?

If both $p$ and $q$ are false then ($p\Rightarrow q$) is true. If either $p$ or $q$ is true then one of ($r\Rightarrow p$) or ($r\Rightarrow q$) is true. If both $p$ and $q$ are true then all are ...
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### Discrete: Boolean Function

~(pV~q) v (~p^~q) is equal to ~p? I know the answer is yes and I've been using DeMorgans initially then distributive law after. However I keep messing up on the algebra. Help is appreciated so I can ...
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### 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 ...
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### 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 ...
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### 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 ...
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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
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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 ...