Show that (p→q)↔(~pvr) is a tautology. I'm stuck to this and I don't know that rules of inference to use
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In words, (p→q) means that, if p is true then so is q. The converse is true: not-p is true (p is false) then not-q is true (q is false). (∽p ∨ r) means not-p or r is true. We have no given premise for r. 

If on the left hand side p is true then not-p is false; on the right hand side though we have not-p. But p is true cannot imply that ∽p is true, so r would have to be true in order to satisfy ⟷. We have no statement for r, so we cannot judge whether or not we have tautology.

If (p→∼r), or (q→∽r), then (∽p ∨ r) is true, because (∽p ∨ r) is the same as (∽p ∨ ∽p) which is tautological. But r must be defined to resolve the problem.

Or have I missed something?

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