Question

show that (p∧q)→(p∨q) is a tautology

How could we solve this without using the truth table ? I couldn't solve it using rules , because it says on the first step using example 3 " truth table "

but how could I solve this without using the table ?

Answer 1

how do we get from:

a -> b to an or statement ... if memory serves

Answer 2

-a v b i think ...

Answer 3

essentially you try to manipulate it thru known properties to show that it is always true regardless of the p,q inputs

Answer 4

(p∧q)→(p∨q)

-(p∧q) v (p∨q)

(-p -∧-q ) v (p∨q)

(-p v -q ) v (p∨q)

-p v -q v p∨q

-pvp v -qvq

(-pvp) v (-qvq)
T v T

Answer 5

Thank you sir.

Answer 6

youre welcome