IST 230 Quiz Lesson 1 – Questions are 10 points each. Chapter 1 Logic 1. Indicat
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Question
IST 230 Quiz Lesson 1 – Questions are 10 points each.
Chapter 1 Logic
1. Indicate clearly which of the following are propositions.
a) Read the textbook!
b) If x is any even integer, then x = 2k + 1, where k is some integer.
c) The first human to set foot on the moon was not Neil Armstrong.
d) 4 x -7 = 10.
e) All continuous functions from the real numbers to the real numbers are differentiable.
2. Define the following propositions:
p : My flight is delayed.
q : There are thunderstorms at the airport.
r : The airport has WiFi.
Translate the following English sentences into logical expressions using the definitions above:
a. My flight is delayed, there are thunderstorms at the airport, and the airport doesn't have Wi-Fi.
b. If there are no thunderstorms at the airport, then my flight is not delayed.
c. The airport doesn't have Wi-Fi and there are thunderstorms at the airport, but my flight is not delayed.
d. The airport does not have WiFi, but my flight is not delayed.
e. My flight is not delayed only if there are no thunderstorms at the airport.
3. Let the domain for the variables x and y be all people in our IST 230 class. Define the predicate K(x,y) to mean "x knows y." Express the following sentences with quantified logical expressions.
a. There is someone in our IST 230 class who knows everybody in our IST 230 class.
b. Nobody in our IST 230 class knows anyone in our IST 230 class.
c. Nobody in our IST 230 class knows everyone in our IST 230 class.
d. There is someone in our IST 230 class whom everyone in our IST 230 class knows.
e. Someone in our IST 230 class knows someone in our IST 230 class.
4. Let be a proposition that is always false, and let be any proposition. Complete the truth table below for .
Explain in words what the (correctly completed) truth table for shows.
5. Use a truth table in form below to show that and are not equivalent. Feel free to make necessary adjustments to the table.
T
T
F
F
6. Tell whether the following two expressions are equivalent by constructing their truth. You may make necessary adjustments to the table provided below. Be sure to explain your answer in words.
logically equivalent to ?
7. Prove or Disprove the following using the laws of propositional logic;
¬p ¬q q p
Explanation / Answer
1) a)it is not a proposition.
because it is not a declarative sentence that result in true or false.
b) it is a propostion because it result in true or false.
c)as the sentence result in false it is a proposition.
d)it is a proposition as it result in false sentence.
e)it is not a proposition as it is not a declarative.
2)a) (p q) ~r
b)~qp
c)(~r q) ~p
d)~r ~p
e)~p~q
4)Let let Letlet
f f f
f t f
5)p ~p p<=>~p
t f f
t f f
f t f
f t f
as the above truth table is a contradiction so these are not logically equivalent.
6)p q r q r p r p q p (qr) (p q)(p r )
t t t t t t t t
t t f f t t t t
t f t f t t t t
t f f f t t t t
f t t t t t t t
f t f f f t f f
f f t f t f f f
f f f f f f f f
therefore the given expressions are logically equivalent.
7)by taking left hand side expression we are going to prove right hand side one
given l.h.s and by using propositonal logic
1)~p~q by using implication in terms of 'or" we get
2)~(~p) ~q and by double negation we get
3)p ~q and now by commutative law we get
4)~q p and now by imlication in terms of 'or' we get
5)qp the final r.h.s
or
by simple the law of contra positive we can explain in a single step.
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