- #1

sjung915

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## Homework Statement

Show that (p ∧ q) → r and (p → r) ∧ (q → r) are not

logically equivalent.

## Homework Equations

a → b = [itex]\neg[/itex]a v b

## The Attempt at a Solution

I'm sorry. I'm completely stumped on how to go about this problem. I'm not asking for the solution since I want to know how to do this instead of just getting the answer. Any help would be appreciated. Thank you.

Here is what I had just so no one thinks I didn't try.

(p ∧ q) → r

=> [itex]\neg[/itex] ( p [itex]\wedge[/itex] q ) [itex]\vee[/itex] r

=> ([itex]\neg[/itex]p [itex]\wedge[/itex] [itex]\neg[/itex]q ) [itex]\vee[/itex] r

=> (switched it around) r [itex]\vee[/itex] ([itex]\neg[/itex]p [itex]\wedge[/itex] [itex]\neg[/itex]q )

=> (distributed) (r [itex]\vee[/itex] [itex]\neg[/itex]p ) [itex]\wedge[/itex] ( r v [itex]\neg[/itex] q)

=> ([itex]\neg[/itex]p v r ) [itex]\wedge[/itex] ([itex]\neg[/itex]q v r )

=> (p -> r ) [itex]\wedge[/itex] (q -> r)

It said disprove but somehow I'm getting that they are L.E.

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