CK-12 Geometry-Concepts

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

TABLE2.15:(continued)

p q ∼q (q∨∼q) p∧(q∨∼q)

F F T T F

Explore More

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

12.

p→∼r

r

∴∼p

13.

∼q→r

q

∴∼r

14.

p→(r→s)

p

∴r→s