- #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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