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Category: Logic

Question-202830

Question Number 202830 by dimentri last updated on 04/Jan/24 $$\:\cancel{\underbrace{ }} \\ $$ Answered by mr W last updated on 04/Jan/24 $${lcm}\left(\mathrm{3},\mathrm{5},\mathrm{7},\mathrm{9}\right)=\mathrm{5}×\mathrm{7}×\mathrm{9}=\mathrm{315} \\ $$$$\Rightarrow{n}=\mathrm{315}{k}−\mathrm{1} \\…

Prove-the-following-is-a-tautology-p-q-p-r-q-r-

Question Number 198750 by depressiveshrek last updated on 24/Oct/23 $$\mathrm{Prove}\:\mathrm{the}\:\mathrm{following}\:\mathrm{is}\:\mathrm{a}\:\mathrm{tautology}: \\ $$$$\left[\left({p}\veebar{q}\right)\wedge\left({p}\Rightarrow{r}\right)\right]\Rightarrow\left({q}\veebar{r}\right) \\ $$ Answered by MathematicalUser2357 last updated on 29/Dec/23 $$\mathrm{Only}\:\mathrm{know}\:\mathrm{until} \\ $$$$=\sim\left[\left({p}\veebar{q}\right)\wedge\left(\sim{p}\vee{r}\right)\right]\vee\left({q}\veebar{r}\right) \\…

Question-198288

Question Number 198288 by Safojon last updated on 16/Oct/23 Answered by mr W last updated on 17/Oct/23 $$\mathrm{4}+{a}={a}\:\mathrm{cosh}\:\frac{{b}}{\mathrm{2}{a}} \\ $$$$\mathrm{11}={a}\:\mathrm{sinh}\:\frac{{b}}{\mathrm{2}{a}} \\ $$$$\left(\mathrm{4}+{a}\right)^{\mathrm{2}} −\mathrm{11}^{\mathrm{2}} ={a}^{\mathrm{2}} \\…