Search & Filtering
A. Write each statement into its symbolic form
x: PJ is a mathematician
y: MJ is a programmer
a. PJ is not a mathematician.
b. PJ is a mathematician while MJ is a programmer.
c. If PJ is a mathematician then MJ is not a programmer.
d. PJ is a mathematician or if PJ is a mathematician then MJ is a
programmer.
e. Either PJ is a mathematician and MJ is a programmer, or neither PJ is a mathematician nor MJ is a programmer.
PREDICATE LOGIC:
A.Write the following predicates symbolically and determine their true value.
Note: Use at least three (3) values for the variables.
1. for every real number x, if x>1 then x – 1 > 1
2. for some real number x, x2 ≤ 0
B. Translate the following English sentence into a symbol. (3 pts each)
1. No one in this class is wearing pants and a guitarist.
Let:
Domain of x is all persons
A(x): x is wearing pants
B(x): x is a guitarist
C(x): belongs to the class
Answer:
2. No one in this class is wearing pants and a guitarist.
Let:
The domain of x is persons in this class
A(x): x is wearing pants
B(x): x is a guitarist
Answer:
3. There is a student at your school who knows C++ but who doesn’t
know Java.
Let:
Domain: all students at your school
C(x): x knows C++
J(x): x knows Java
Answer:
PREDICATE LOGIC.(25 pts)
A. Let P(x) be the statement x 2 > x4. If the domain consists of the integers,
what are the truth values?
1. P(0)
2. P(-1)
3. P(1)
4. P(2)
5. ∃xP(x)
6. ∀xP(x)
PROPOSITIONAL LOGIC:
A. Let p, q and r denotes the following statements:
p: A square has four equal side
q: Rectangle has 2 parallel sides
r: A square is a rectangle.
1. Express each of the following into English sentence.
a. r ^ q → p
b. p̅ → q
c. q → p̅ v r
2. Write T if the above item is true and F if it false. Show solution. (3 pts
each)
a.
b.
c
B. Show whether or not p ↔ q ≡ (p → q) ^ (q → p)
C. Find the converse, inverse and contrapositive of the implication: “If today is
Monday then, I have an exam today.” (3 pts each)
1. Inverse:
2. Converse:
3. Contrapositive:
What is the symbolic form of the statement, “No one in this class is wearing pants and a guitarist” if the domain of x is persons in this class, A(x): x is wearing pants and B(x): x is a guitarist?
RULE OF INFERENCE:
Determine if the following argument is valid. Explain by using rule of
inference. (5 pts each)
1. If you perform every programming problem in the module, then you
will learn programming. You learned programming. Therefore, you
perform every programming problem in the module.
2. Not everyone likes to go to the hospital; hence, there is someone
who does not like to go to the hospital
RULE OF INFERENCEe
A. What rule of inference is used in each of the following arguments?
Show solution. (5 pts each)
1. If I will read my modules, then I can answer all the activities. If I can
answer all the activities, then I will get high scores. Therefore, if I will
read my modules, then I will get high scores.
2. Rizza is an IT student. Therefore, Rizza is either an IT student or a
programmer
3. If it is national holiday, then school is closed. It is national holiday.
Therefore, the school is closed.
4. If Ann does not love numbers or if Ann does not love programming.
If Ann loves numbers, then she can be a mathematician. Therefore,
Ann can be a mathematician.
Let S = ℤ+, a ~ b if a − b is divisible by 2. Is S an equivalence relation?
Let p denote He is rich and let q denote He is happy. Write each statement in symbolic form using p and q. Note
that He is poor and He is unhappy are equivalent to ¬p and ¬q, respectively.
(a) If he is rich, then he is unhappy. (c) It is necessary to be poor in order to be happy.
(b) He is neither rich nor happy. (d) To be poor is to be unhappy
1. Given A = (2, 4, 6, 8} and B = {3, 4, 5, 6}, determine:
a. A ∪ B b. A ∩ B
2. Given A = {3, 5, 7, 9} and B = {4, 5, 6, 7}, determine:
a. A - B
b. B - A
c. A ∩ B
