If P then QDate: 08/29/97 at 03:40:07 From: Harout Jarchafjian Subject: If p then q Our math book states that the implication of if p then q, the truth table, is p = true, q = true, statement = true p = true, q = false, statement = false p = false, q = doesn't matter, statement = true I don't understand how if p is false then regardless of q, the statement is true. My math book gives no examples of this. Can you please give an example? Thank you, Harout Jarchafian Date: 08/29/97 at 19:01:09 From: Doctor Anthony Subject: Re: If p then q p implies q can be written p -> q This means that p is a subset of q. Draw a venn diagram with the set p completely enclosed within set q. Draw a box enclosing set q to represent the universal set. Then the area inside both p and q is pq area outside p but still inside q is p'q area outside q but inside the box is p'q' Then 1 represents the universal set and adding the three areas gives the universal set, so pq + p'q + p'q' = 1 Now draw up the truth table for p -> q p q p -> q --------------------- 0 0 1 This line is p'q' 0 1 1 This line is p'q 1 0 0 This line is pq' (does not contribute) 1 1 1 This line is pq ---------------------- From this table you can see that p=0 (i.e. p'=1) always gives p->q = 1 This is equivalent to saying p = false means p->q is always true. -Doctor Anthony, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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