# Tagged Questions

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### The negation of an implication statement

$$\neg(A \longmapsto B)\lor \neg B$$ Does this this expression simplify to:? $$\neg A\longmapsto\neg B\lor \neg B$$ Which further simplifies to: $$\neg A\longrightarrow\neg B$$
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### Truth-functional completeness

Let the statement $?PQR$ be determined by the following truth-table. ...
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### Boolean Logic - Reduction - $a \vee (a \wedge b) = a$

How would I simplify / reduce the following equation using boolean identities/proofs? $$a \vee (a \wedge b) = a$$ So far I've used the distributivity identity and got $$(a\vee a) \wedge (a\vee b)$$ I ...
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### Do brackets around negation signify negating the input or output - Boolean Algebra Logic Circuits

I know that $\overline{p + q}$ will result in the input to the logic gate being p, and q, and we can negate this by using an or gate, followed by a not gate, or we can just use a nor gate. However, ...
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### How can i turn the Boolean Equation pq+r into a switch circuit?

How can I turn the Boolean Equation $pq+r$ into a switch circuit? I have synthesized this and drawn the NOR gates circuit however I'm not sure how to go about drawing/constructing the switch circuit.
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### Applying De Morgans Laws to $a+bc+\overline{a}b\overline{c}d$ in terms of the NOR operator

I need to synthesize $f=a+bc+\overline{a}b\overline{c}d$ into the NOR form. Can I split this since I know that $a+bc=(a+b)(a+c)=\overline{\overline{a+b}+\overline{a+c}}$? I'm just not sure how to go ...
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### Applying De Morgan's to express $pq+r$ in terms of NOR operator

In Boolean Algebras I have $pq+r$ which I think is the same as $(p+r)(q+r)$. Now, I need to use De Morgan's laws to synthesize this into the NOR form but I am not sure how to apply the laws here.
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### Boolean Expression simplification help

Hi I am new to the board. Taking a computer architecture course and I am having trouble understanding further simplification on a question I got on a previous quiz. When I type in the expression ...
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The covering rule is: $$B \bullet (B+C) = B$$ and $$B+(B \bullet C)=B$$ So does it follow from this rule that: $$B \bullet A \bullet \bar{C} + B \bullet D \bullet\bar{F} = B \bullet ... 0answers 54 views ### Simplify Product of Sums Similar question to: Boolean Algebra - Product of Sums I was given a truth table and asked to give the sums-of-products and the product-of-sums expressions. I reduced the sums-of-products ... 3answers 62 views ### Construct XNOR with only OR gates Is it possible to construct the XNOR gate which is given as, a XNOR b = (a AND b) OR (~a AND ~b), by using only OR gates. So from the definition, the question boils down to: can you construct the AND ... 1answer 50 views ### Alternative to xor(A,B,C) How can we make a comprehensive statement, which will correspond to the truth table of xor (A, B, C) by combining logical operators AND (&), OR (|), XOR (xor) and NOT (!)? 1answer 61 views ### Convert a boolean function into K-map I would like to know how can I convert the following boolean function into a truth table and accordingly construct the k-map$$F = A'B'C'+B'CD'+A'BCD'+AB'C'$$thanks in advance :) 0answers 61 views ### Boolean algebra - cube - minimal disjunctive normal form I have a test coming up and I would like to know how to solve these kinds of problems. This is the description: ... 3answers 131 views ### Peculiar examples to the Stone Representation Theorem The Stone Representation theorem states that every Boolean algebra is isomorphic to a field of sets. That is, a Boolean algebra whose elements are sets, and sums, products, negation are union, ... 5answers 69 views ### If one of the hypotheses holds, then one of the conclusions holds. (looking for a proof) Using a huge truth table, I proved the theorem below. I cannot find a more elegant proof. I tried to rewrite expressions; e.g. using the distributive laws and the laws of absorption - to no avail. Is ... 3answers 59 views ### Proving \neg A\vee(A\wedge \neg B)= \neg A \vee \neg B. How do I prove using boolean algebra that \neg A\vee(A\wedge \neg B)= \neg A \vee \neg B? I can see it in the logic table and it is logical, but I can't prove it mathematically. 1answer 48 views ### How can I simplify this boolean equation for the multiplexer a little further? I've obtained a formula through cannonical representation, which is:$$A\cdot \overline{B\cdot S}+A\cdot B\cdot \overline{S}+\overline{A}\cdot B\cdot S+A\cdot B \cdot S$$And I'm trying to simplify ... 1answer 61 views ### Checking Boolean Algebra work - Simplification I am currently working on an assignment for a CE class I am taking, and I wanted to know if I have been simplifying these equations correctly. I'm supposed to reduce them to a sum of products. 1) ... 1answer 88 views ### Conjunctive Normal Form vs Product of Sums I am confused as to what the difference between Conjunctive Normal Form and Product of Sums is. Can someone explain what is different about them? It seems like they both only use groups of OR ... 2answers 78 views ### How to construct the truth table for a combinational circuit I am trying to construct the truth table for a combinational circuit with the following conditions : A) Room with 4 doors , 1 light, a switch near each door that controls the light (4 in total) B) ... 1answer 57 views ### Boolean Queries in First Order Logic I understand first order logic and how its constructed but I have some trouble understanding how the following statement and its FO query are formed. This is from a book. ... 2answers 40 views ### What is a Boolean Function? Please explain to me what a Boolean function is, and how do I make an expression. If the statement states that f="she is out of work" and s="she is spending more", how can I write symbolically ... 1answer 44 views ### A problem with a boolean function. This is one of my assignment problem and I almost finished others. This question confused me for quite a long time and now I get nothing about that. I did understand what is an increasing function ... 1answer 151 views ### convert circuit to nor only gates for an assignment I need to convert a circuit to NOR gates only circuit. (A+B)C + D I know that morgan's theorem states: (a) (A+B)'=A'B' (b) (AB)'=A'+B' I've seen online how to convert some ... 3answers 153 views ### Using rules of inference (Leibniz) to prove theorems. Leibniz: If A \equiv B is a theorem, then so is C[p:= A] \equiv C[p:= B]. Note: p is "fresh" means p doesn't occur in A, B, C. I am trying to understand how to use Leibniz rule of inference for ... 1answer 46 views ### Boolean equation simplification This is the problem: XY’ + XYZ + XY'Z= X + Y'Z And so far I have this, XY’ + XYZ + XY'Z= X + Y'Z X(Y’ + YZ + Y’Z) Factor out X X(Y’ + Z + Y’Z) De Morgan Any tips on how to proceed? I know ... 3answers 46 views ### Simplify this Logic Function? Have a Hardware Lab to do, and I need to reduce the following function before I actually hook it up to the Logic Trainer. (not ac) + (abc) + (a not c) Or: \lnot (a \land c) \lor (a \land b ... 1answer 77 views ### Simplification of a Boolean Expression I want to simplify this expression: ACD' + E(A+C)(A'+D') + A'C . The result must be a product of sums, where every sum should be consisted of just two variables. For example (A+B)(C+A)(Z+Y) ... ... 2answers 50 views ### simplify the boolean expression I'm fairly new too boolean algebra. I've tried simplifying this equation but I'm not quite sure if I've done it correctly. Simplify to 1 literal, (X + Y + Y'Z)(Y + X)(Y + X') My attempt: ... 2answers 108 views ### Prove (A \backslash B)'\backslash (B \backslash A) = B \backslash A Let A and B be subsets of some universal set. Prove that (A \backslash B)'\backslash (B \backslash A) = B \backslash A Given: Definition 3.3.1 states that A and B are sets. The complement ... 4answers 250 views ### Prove A \subseteq B \cap C if and only if A \subseteq B and A \subseteq C Prove the following for any sets A,B and C. This is actually two sets that I'm trying the prove. The title character restriction wouldn't allow me to post both at the same time. a. A \subseteq ... 2answers 243 views ### Exercise regarding boolean algebra? We need to simplify AC+A'B'C Y=A'B' +A'B C'+(A+C')' For (1) I wrote C(A+A'B') but the result must be AC+ B'C. How do I get that to happen? I tried to simplify (2) using deMorgan but no ... 2answers 334 views ### Verify a Tautology without a truth table. Verify that the following are tautologies. Do not make truth tables. a. \lnot(\lnot) P \leftrightarrow P The first question is just a double negation law. So, if I have to take the left side and ... 3answers 72 views ### Prove the following f_{(A \cup B)}(x)=f_A(x)+f_B(x)-f_A(x)\cdot f_B(x) There is option to prove the following with truth table?$$f_{(A \cup B)}(x)=f_A(x)+f_B(x)-f_A(x)\cdot f_B(x) I would like to get some hints how to do it in formal way(not truth table) thanks!
So i want to find the DNF and CNF of : $x \oplus y \oplus z$ . I tried by using $x \oplus y = (\neg x\wedge y) \vee (x\wedge \neg y)$ but it got all messy and stuff, I also plotted it in ...