# Exercise ID368

Thinking Operations → Logic → Basic Logical Operations
[Level: ] [Number of helps: 1] [Number of pictures: 0] [Number of steps: 18] [Number of characters: 342]

Határozza meg a következő kifejezések igazságértékét:

$p\equiv \frac{3+2x}{3}-\frac{2-3x}{4}=\frac{29}{24};x=0,5$

$q\equiv 3\left(5-y\right)-2\left(y-1\right)=1+3y;y=2$Ezt követően határozza meg az alábbi két kifejezés igazságértékét is:

a) $\left(p\vee q\right)\wedge p$

b) $\left(p\wedge q\right)\vee p$

${p}{\equiv }\frac{3+2·0,5}{3}-\frac{2-3·0,5}{4}{=}\frac{29}{4}\phantom{\rule{0ex}{0ex}}$ ${p}{\equiv }\frac{3+1}{3}-\frac{2-1,5}{4}{=}\frac{29}{4}\phantom{\rule{0ex}{0ex}}$ ${p}{\equiv }\frac{4}{3}-\frac{0,5}{4}{=}\frac{29}{4}\phantom{\rule{0ex}{0ex}}$ ${p}{\equiv }\frac{4}{3}-\frac{1}{4}·\frac{1}{2}{=}\frac{29}{4}\phantom{\rule{0ex}{0ex}}$ ${p}{\equiv }\frac{4}{3}-\frac{1}{8}{=}\frac{29}{4}\phantom{\rule{0ex}{0ex}}$ ${p}{\equiv }\frac{4}{3}-\frac{1}{8}=\frac{4·8-3·1}{24}=\frac{32-3}{24}=\frac{29}{24}{=}\frac{29}{24}\phantom{\rule{0ex}{0ex}}$ ${p}{\equiv }\frac{29}{24}{=}\frac{29}{24}⇒p=\top \phantom{\rule{0ex}{0ex}}$ ${q}{\equiv }3\left(5-y\right)-2\left(y-1\right){=}{1}{+}{3}{y};y=2\phantom{\rule{0ex}{0ex}}$ ${q}{=}3\left(5-2\right)-2\left(2-1\right){=}{1}{+}{3}{·}{3}\phantom{\rule{0ex}{0ex}}$ ${q}{=}3·3-2·1{=}{1}{+}{3}{·}{2}\phantom{\rule{0ex}{0ex}}$ ${q}{=}9-2{=}{1}{+}{6}\phantom{\rule{0ex}{0ex}}$ $\phantom{\rule{0ex}{0ex}}$ $\phantom{\rule{0ex}{0ex}}$$\left(p\vee q\right)\wedge p=\top \phantom{\rule{0ex}{0ex}}$ $\phantom{\rule{0ex}{0ex}}$ $\phantom{\rule{0ex}{0ex}}$$\left(p\wedge q\right)\vee p=\top \phantom{\rule{0ex}{0ex}}$
HELP AVAILABLE!
 P Q P ∨ Q ⊤ ⊤ ⊤ ⊤ ⊥ ⊤ ⊥ ⊤ ⊤ ⊥ ⊥ ⊥
 P Q P ∧ Q ⊤ ⊤ ⊤ ⊤ ⊥ ⊥ ⊥ ⊤ ⊥ ⊥ ⊥ ⊥