Question and Answers Forum

All Questions      Topic List

Algebra Questions

Previous in All Question      Next in All Question      

Previous in Algebra      Next in Algebra      

Question Number 191735 by Spillover last updated on 29/Apr/23

$$Verifythat$$$$⌝(p\to q)\to \left(p{\wedge }^{⌝}q\right)istautologyusinglawsof$$$$algebra$$

Answered by manxsol last updated on 30/Apr/23

$$\sim (\sim pq)\to (p\sim q)$$$$(\sim pq)(p\sim q)$$$$(\sim pq)p\}(\sim pq\sim q)$$$$\left\{\mathit{V}q\right\}\left\{\mathit{V}q\right)$$$$VV=Vtautologia$$$$p\to q=\sim pq$$$$distributiva$$$$p\left(qr\right)=pq)\left(pr\right)$$

Answered by aba last updated on 30/Apr/23

$$\overline{)\begin{array}{ccccc}\mathrm{p}& \mathrm{q}& \rceil (\mathrm{p}\to \mathrm{q})& \mathrm{p}\wedge \rceil \mathrm{q}& \rceil (\mathrm{p}\to \mathrm{q})\to (\mathrm{p}\wedge \rceil \mathrm{q})\\ 0& 0& 0& 0& 1\\ 0& 1& 0& 0& 1\\ 1& 0& 1& 1& 1\\ 1& 1& 0& 0& 1\end{array}}$$

Commented by Spillover last updated on 30/Apr/23

$$readthequestioncarefull.thequestionsays$$$$usethelawsofalgebra.Thanksforyoursolution$$

Commented by aba last updated on 30/Apr/23

$$\mathrm{i}\mathrm{know}$$

Answered by Spillover last updated on 30/Apr/23

$$\sim (p\to q)\to (p\wedge \sim q)$$$$\sim [(\sim p\vee q)\vee \sim (p\wedge \sim q)$$$$p\wedge \sim q\vee \sim p\vee q$$$$p\vee \sim p\sim q\vee q$$$$T\vee T$$$$T$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com