Question
1. Use a truth table to find if the following is valid or not valid: p r q r q r Therefore, p Valid Not
1. Use a truth table to find if the following is valid or not valid: p r q r q r Therefore, p
Valid
Not Valid
Discrete Math
2. Indicate whether each expression is an equivalence of the following:
p q
p q
p q
(p q)
(p q) (p q)
(p q)
3. For the given values for p, q, and r, what is the result of the following proposition. A truth table might be helpful here.
(r q) (p r)
p=T q=T r=T
p=T q=F r=T
p=T q=F r=F
p=F q=T r=T
p=F q=F r=F
QUESTION 5 For the statement P(x,y) meaning x+2y = xy, determine if the following are true or false.
P(0,0)
P(1,-1)
yP(3,y)
xP(x,2)
x yP(x,y)
QUESTION 6 Indicate whether each of the following is a proposition:
3 + 2 = 9
Get your raincoat
It is raining.
57
purple
QUESTION 7
For the premises "Someone in this class passed the exam", and "Everyone in this class read the textbook" imply the conclusion "Someone that read the textbook passed the exam". If C(x) is the predicate "x is in this class", R(x) is the predicate "x has read the textbook" and P(x) is the predicate "x passed the exam", what are the reasons each of the following steps can be deemed valid:
1. x(C(x) P(x))
2. C(a) P(a)
3. C(a)
4. x(C(x) R(x))
5. C(a) R(a)
6. R(a)
7. P(a)
8. P(a) R(a)
9. x(P(x) R(x))
10. C(a) R(a)
A. Premise
B. Addition
C. DeMorgans Law
D. Modus Tollens
E. Modus Ponens
F. Conjunction
G. Existential Instantiation
H. Existential Generalization
I. Universal Instantiation
J. Universal Generalization
K. Simplification
QUESTION 8 Every proposition can be expressed in terms of AND, OR, and NOT. What proposition represents the following truth table?
p q
p q
p q
(p q) (p q)
(p q) (p q)
QUESTION 9
Indicate whether the following are Tautologies or Contradictions:
p p
p p
p (q q)
p (q q)
((p q) q) p
QUESTION 10
For the premises "Everyone who read the textbook passed the exam", and "Ed read the textbook" imply the conclusion "Ed passed the exam". If R(x) is the predicate "x has read the textbook" and P(x) is the predicate "x passed the exam", what are the reason each of the following steps can be deemed valid:
1. x(R(x) P(x))
2. R(Ed) P(Ed)
3. R(Ed)
4. P(Ed)
5. R(Ed) P(Ed)
A. Premise
B. Conjunction
C. Addition
D. Simplification
E. Modus Ponens
F. Modus Tollens
G. DeMorgans Law
H. Universal Instantiation
I. Existential Instantiation
QUESTION 11 What is the negation of the following sentence:
It is Thursday and it is cold.
It is not Thursday and it is cold.
It is Thursday and it is not cold.
It is not Thursday and it is not cold.
It is not Thursday therefore it is not cold.
It is not Thursday or it is not cold.
QUESTION 14 Match the following statements with predicates and any necessary quantifiers:
Every Razzma is a Frat.
No Razzma is a Frat.
There is at least one Razma that is a Frat
There is a Razma that every Frat.
Some Razma are Green Frat.
A. R(x) F(x)
B. x(R(x) F(x))
C. x(R(x) F(x))
D. x(R(x) F(x))
E. x(R(x) F(x))
F. yx(F(x) R(x,y))
G. x(R(x) F(x) G(x))
H. xy(R(x) F(y) G(y))
I. xy(R(x) F(y) G(x,y))
J. xy(R(x) F(y) G(x,y))
QUESTION 15 Indicate which of the following are equivalent to: A Yes B No
If Joe is going to the game, then I am going bowling.
Joe is going to the game if I am going bowling.
I am going bowling if Joe is going to the game.
Joe is going to the game implies I am going bowling.
Joe is going to the game whenever I am going bowling.
I am going bowling whenever Joe is going to the game.
Step by Step Solution
There are 3 Steps involved in it
Step: 1
Get Instant Access to Expert-Tailored Solutions
See step-by-step solutions with expert insights and AI powered tools for academic success
Step: 2
Step: 3
Ace Your Homework with AI
Get the answers you need in no time with our AI-driven, step-by-step assistance
Get Started