hey friends,

please help me out with this question! thanks lots! (Happy)

show that (p→q)∧(p→r) and p→(q∧r) is logically equivalent

thanks in advance!

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- August 30th 2011, 07:48 AMllapkanpropositional logic
hey friends,

please help me out with this question! thanks lots! (Happy)

show that (p→q)∧(p→r) and p→(q∧r) is logically equivalent

thanks in advance!

- August 30th 2011, 08:06 AMPlatoRe: propositional logic
- August 30th 2011, 09:52 AMHallsofIvyRe: propositional logic
Another way to do this is to construct a "truth table". p, q, and r can each be "T" or "F" so there are cases.

If p= q= r= T, then is true and is true so is true. Also then [tex]q\wedge r[/itex] is true so is true. Since they are both true in this case.

If p= F, which includes 4 of the 8 cases, each of , , and is true because " " is true no matter what x is.

Now show they are the same in the other 3 cases.