CK-12 Geometry Concepts

2.6. Truth Tables http://www.ck12.org

TABLE2.13:

p ∼p p∧∼p

T F F

F T F

2. First, make columns forpandq, then add in∼pand∼q. Finally, evaluate∼p∨∼q.

TABLE2.14:

p q ∼p ∼q ∼p∨∼q

T T F F F

T F F T T

F T T F T

F F T T T

3. First, make columns forpandq, then add in∼qandq∨∼q. Finally, evaluatep∧(q∨∼q).

TABLE2.15:

p q ∼q (q∨∼q) p∧(q∨∼q)

T T F T T

T F T T T

F T F T F

F F T T F

Practice

Write a truth table for the following variables.

1.(p∧q)∨∼r

2. p∨(∼q∨r)


3. p∧(q∨∼r)


4. The only difference between #1 and #3 is the placement of the parenthesis. How do the truth tables differ?


5. When isp∨q∨rtrue?


6. p∨q∨r
   7.(p∨q)∨∼r
   8.(∼p∧∼q)∧r
   9.(∼p∨∼q)∧r

Is the following a valid argument? If so, what law is being used? HINT: Statements could be out of order.

10.

p→q

r→p

∴r→q

11.

p→q

r→q

∴p→r