Question

Disjunctions
(a)\[(\pi>3)\vee(\pi>10)\]
(b)\[(x<0)\vee(x>0)\]
(c)\[(x=0)\vee(x>0)\]
(d)\[(x>0)\vee(x\geq0)\]
(e)\[(x>3)\vee(x^2>9)\]

Answer 1

(a)
\[(\pi>3)\vee(\pi>10)\quad\longrightarrow\quad \pi>10\]
(b)
\[(x<0)\vee(x>0)\quad\longrightarrow\quad x\neq0\]
(c)
\[(x=0)\vee(x>0)\quad\longrightarrow\quad x\geq 0\]
(d)
\[(x>0)\vee(x\geq0)\quad\longrightarrow\quad x\geq0\]
(e)
\[(x>3)\vee(x^2>9)\quad\longrightarrow\quad (x>3)\vee[x>3 \vee x<-3]\]\[\qquad\qquad\qquad\qquad\qquad\longrightarrow\quad (x>3)\vee (x<-3)\]\[\qquad\qquad\qquad\qquad\qquad\longrightarrow\quad (x^2>9)\]

Answer 2

please check my work

Answer 3

how (a) ??
pi>3 ?

Answer 4

hmm yeah

Answer 5

rest are correct.

Answer 6

thank you !