p-q-p-q-simplify-

Question Number 148051 by abdurehime last updated on 25/Jul/21

$$\rightharpoondown\left(\rightharpoondown\mathrm{p}\rightarrow\mathrm{q}\right)\vee\left(\mathrm{p}\wedge\rightharpoondown\mathrm{q}\right)\: \\ $$$$\mathrm{simplify} \\ $$

Commented by abdurehime last updated on 25/Jul/21

$$\mathrm{please}\:\mathrm{sir}\:\mathrm{help}\:\mathrm{me} \\ $$

Commented by abdurehime last updated on 25/Jul/21

$$\mathrm{why}\:\mathrm{not}\:\mathrm{jump}\:\mathrm{my}\:\mathrm{question} \\ $$

Answered by iloveisrael last updated on 25/Jul/21

p→q =⇁p∨q ⇁p→q=p∨q ⇁(⇁p→q)= ⇁p∧⇁q ⇁(⇁p→q)∨(p∧⇁q)= (⇁p∧⇁q)∨(p∧⇁q)= ⇁q∧(⇁p∨p) = ⇁q

$$\mathrm{p}\rightarrow\mathrm{q}\:=\rightharpoondown\mathrm{p}\vee\mathrm{q} \\ $$$$\rightharpoondown\mathrm{p}\rightarrow\mathrm{q}=\mathrm{p}\vee\mathrm{q} \\ $$$$\rightharpoondown\left(\rightharpoondown\mathrm{p}\rightarrow\mathrm{q}\right)=\:\rightharpoondown\mathrm{p}\wedge\rightharpoondown\mathrm{q} \\ $$$$\rightharpoondown\left(\rightharpoondown\mathrm{p}\rightarrow\mathrm{q}\right)\vee\left(\mathrm{p}\wedge\rightharpoondown\mathrm{q}\right)= \\ $$$$\:\left(\rightharpoondown\mathrm{p}\wedge\rightharpoondown\mathrm{q}\right)\vee\left(\mathrm{p}\wedge\rightharpoondown\mathrm{q}\right)= \\ $$$$\:\rightharpoondown\mathrm{q}\wedge\left(\rightharpoondown\mathrm{p}\vee\mathrm{p}\right)\:=\:\rightharpoondown\mathrm{q}\: \\ $$$$ \\ $$

Commented by abdurehime last updated on 25/Jul/21