Question

Prove:

\[\Large (p \rightarrow q) \wedge (q \rightarrow r) \rightarrow (p\rightarrow r) \equiv T\]

Answer 1

\[(p \rightarrow q)and(q \rightarrow r)\]equivalent to
\[p \rightarrow r\]

Answer 2

how??

Answer 3

Do you know the solution or you just know how to solve it?

Answer 4

what's the difference between those two?

Answer 5

You have to know the priority of the logical operations and \(p \rightarrow q=¬p\vee q\).

Answer 6

hmm that part i know

Answer 7

we will use an 8 row table to do this

Answer 8

no truth tables

Answer 9

p)i solve the question ,q)you give me medal,r)i log out.
does it mean that if i solve th question then i log out
p implies r

Answer 10

....nice star trek lesson.....

Answer 11

rules,
i just cpied it from a pdf

Answer 12

so...all those were to prove \((p \rightarrow 1) \wedge (q\rightarrow r) \equiv p \rightarrow r\)

Answer 13

that's q not 1

Answer 14

is p-> p = T?

Answer 15

solution

Answer 16

yes they were proving that withut tables as you said

Answer 17

yes p=>p is true and thats why that statement is true

Answer 18

i think i am having good practice

Answer 19

that's what you get for hanging out with me

Answer 20

lol but why dont you like tables

Answer 21

you said you use lateX to type this

Answer 22

because there's no thrill in proving by tables...

Answer 23

i also dont like them its not abstract

Answer 24

\[(p→q)∨(p→r)≡p→(q ∨ r)\]

Answer 25

how wuld you prove this without table