# Tagged Questions

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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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### DNF and CNF logic problem

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 ...
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### Logic boolean algebra problem

so I have to prove that these equations : are equivalent?
### Write $p \rightarrow \lnot q$ in CNF form with only and ,or and brackets
Write $p \rightarrow \lnot q$ in CNF form with only and, or, and/or brackets How on earth would I even do this? Completely lost! Any help appreciated.