- #1
bonfire09
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Homework Statement
(b) Show that (p → q) ∨ (p→ r) is equivalent to p → (q ∨ r).
Homework Equations
the ~ means negate
The Attempt at a Solution
Im not sure if i did this correctly
(p → q) ∨ (P → r)
(~p∨q) ∨ (~p∨r) used the conditional law p→q equivalent to ~p∨q
((~p∨q)∨~p)∨((~p∨q)∨r)) distributive law
(~p∨q)∨(~p∨q)∨r
(~p∨q)∨r
~p∨(r∨q) associative law
p →(q∨r)