homework2

compared with
Key
This line was removed.
This word was removed. This word was added.
This line was added.

Changes (39)

View Page History
*1*. # Which of the following sentences are propositions?  What are the truth values of those that are propositions?
# ## Richmond is the capital of Virginia.
# ## 2 + 3 = 7.
# ## Open the door.
# ## 5 + 7 < 10.
# ## The moon is a sattelite of the earth.
# ## _x_ + 5 = 7.
# ## _x_ + 5 > 9 for every real number _x_.

*2.* # What is the negation of each of the following propositions?
# ## Norfolk is the capital of Virginia.
# ## Food is not expensive in the United States.
# ## 3 + 5 = 7.
# ## The summer in Illinois is hot and sunny.

*3*. Let _p_ and _q_ be the propositions

# Let _p_ and _q_ be the propositions: _p_: Your car is out of gas. _q_: You can't drive your car. Write the following propositions using _p_ and _q_ and logical connectives.
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; _p_: ## Your car is not out of gas.
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; _q_: You can't drive your car.

&nbsp;&nbsp;&nbsp; Write the following propositions using _p_ and _q_ and logical connectives.

&nbsp;&nbsp;&nbsp; a) Your car is not out of gas.
&nbsp;&nbsp;&nbsp; b) ## You can't drive your car if it is out of gas.
&nbsp;&nbsp;&nbsp; c) ## Your car is not out of gas if you can drive it.
&nbsp;&nbsp;&nbsp; d) ## If you can't drive your car then it is out of gas.

*4*. # Determine whether each of the following implications is true or false.

&nbsp;&nbsp;&nbsp; a) ## If 0.5 is an integer, then 1 + 0.5 = 3.
&nbsp;&nbsp;&nbsp; b) ## If cars can fly, then 1 + 1 = 3.
&nbsp;&nbsp;&nbsp; c) ## If 5 > 2 then pigs can fly.
&nbsp;&nbsp;&nbsp; d) ## If 3*5 = 15 then 1 + 2 = 3.

*5.* # State the converse and contrapositive of each of the following implications.
# ## If it snows today, I will stay home.
# ## We play the game if it is sunny.
# ## If a positive integer is a prime then it has no divisors other than 1 and itself.

*6.* # Construct a truth table for each of the following compound propositions.

&nbsp;&nbsp; a)&nbsp; ## _p_ !and.gif! !not.gif! _p_
_&nbsp;&nbsp;_ c) (_p_ !or.gif! !not.gif! _q_) !imp.gif|width=32,height=32! _q_
_&nbsp;&nbsp;_ e) (_p_ !imp.gif|width=32,height=32! _q_) !eqv.gif|width=32,height=32! ( !not.gif|width=32,height=32! _q_ !not.gif! _p_)
## (_p_ !or.gif! !not.gif! _q_) !imp.gif! _q_
## (_p_ !imp.gif! _q_) !eqv.gif! ( !not.gif! _q_ !not.gif! _p_)