SALAZAR COLLEGES OF SCIENCE AND INSTITUTE OF TECHNOLOGY
Madridejos Campus
Midterm Exam In Math 104 (Logic & Set Theory) BSED 1
Name : __________________________________ Score __________ Equivalent : ___________
I. Identify the following.
________________ 1. These are used to describe one of the most important concepts in
Mathematics like function.
________________ 2. It is a branch of Mathematical logic where we learn sets and their
properties.
________________ 3. All the elements of the set are listed, separated by a comma and enclosed
between curly braces.
________________ 4. Any set that contains all the set under consideration.
________________ 5. When all the elements of set A belong to set B.
________________ 6. All the elements have a common property. This property is not applicable
to the objects that do not belong to the set.
________________ 7. Sets can be represented in two ways.
________________ 8.
________________ 9. The four important set operations that are widely used.
________________10.
________________11.
________________12.
________________13. A set that has only one element.
________________14. Set A has all the elements which are even prime numbers less than 50.
________________15. The set of natural numbers.
II. Solve operations on set.
1. If A = {a, b, c, d, e}, B = {a, e, i, o, u}, U = {a, b, c, d, e, f, g, h, i, j, k, l, o, u}. Perform the
following operations on sets and find the solutions.
a) A ∪ B
b) A ∩ B
c) A′
d) A - B
2. If A = {2,4,6,8,10} and B = {2,3,5,7}. Find A ∩ B.
3. Let A and B be two finite sets such that n(A) = 20, n(B) = 28 and n(A ∪ B) = 36,
find n(A ∩ B).
4. If n(A - B) = 18, n(A ∪ B) = 70 and n(A ∩ B) = 25, then find n(B).
5. In a school, every student plays either football or soccer or both. It was found that 200 students
played football, 150 students played soccer and 100 students played both. Find how many
students were there in the school using the set operation formula. And illustrate the answer in a
Venn diagram.
III. Construct a compound proposition in a given statement.
p= I love Teaching
q= I love to sketch
r= I am a scientist
1. P ˄ ˜ r
2. P –› r
3. P ˄ q –› r
4. ˜ r –› ˜ p
5. ˜ q ˄ ˜ p –› r
IV. Translate the following English sentences into Logic forms.
1. Hiking is not safe on the trail whenever grizzly bears have been seen in the area and berries are
rip along the trail.
2. You are not allowed to watch adult movies if your age is less than 18 years, or you have no age
proof.
3. If you are a computer science major or you are not a freshman, then you can access the
internet from campus.
4. If it is not raining, then the home team does not win.
5. If I will go to Bea or to the country, I will not go shopping.
