QUESTION 1:

Which of the following statement/s is or are correct?

i. Consider the set of students who are enrolled in a Science course and the set of Science faculty members for thefirst semester of the academic year 2017-2018 in a university. Suppose we define a relation between the two sets by saying that a student corresponds to a Science faculty member if the student is currently enrolled in the said course taught by that faculty member. This relation is, at all times, a function.

ii. A relation is possibly a function.

iii. A function is necessarily a relation.

CHOICES:

A. i and ii only

B. ii and iii only

C. i and iii only

D. i, ii, and iii

QUESTION 2:

Which of the following accurately defines the complement of a given set, say A?

CHOICES:

A. {x | x U and x A}

B. {x | x U and x A}

C. {x | x U and x A}

D. {x | x U and x A}

FOR QUESTIONS 3-9, please consider the following functions:

f(x) = 3x + 1 h(x) = x (square root of x)

g(x) = 1 - 3x p(x) = 2x² + 5x - 3

QUESTION 3:

Which is equal to (fg)(x)?

CHOICES:

A. 9x² - 1

B. 1 - 9x²

C. 9x² + 1

D. 9x² + 18x - 1

QUESTION 4:

Which is equal to (p + g)(x)?

CHOICES:

A. 2x² + 8x - 2

B. 2x² + 2x - 2

C. 2x² + 8x + 2

D. 2x² + 8x + 2

QUESTION 5:

Which is equal to (g/h) (x)?

CHOICES:

A. x - 3xx

B. x/x - 3xx

C. x/x - 3x

D. x-3x / x

QUESTION 6:

Which is equal to (f - p)(x)?

CHOICES:

A. 4 - 2x - 2x²

B. 2 - 2x - 2x²

C. 2 + 2x - 2x²

D. 4 + 2x - 2x²

QUESTION 7:

Which is the range of h(x)?

CHOICES:

A. All Real Numbers

B. All Real Numbers except zero

C. All positive Real Numbers

D. All non-negative Real Numbers

QUESTION 8:

Which is the range of g(x)?

CHOICES:

A. All Real Numbers

B. All Rational Numbers

C. All Integers

D. All Whole Numbers

QUESTION 9:

Which is the range of (f + g) (1) ?

CHOICES:

A. 8

B. 1

C. 2

D. 0

QUESTION 10:

Which of the following is/are NOT a proposition?

i. Will u marry me?

ii. Mount Everest is in Europe.

iii. Read the instructions carefully.

CHOICES:

A. i only

B. i and ii only

C. i and iii only

D. i, ii, and iii

QUESTION 11:

Consider the following propositions.

p: 2 is the smallest prime

q: 6 is a perfect square

Represent the proposition "2 is the smallest prime but 6 is not a perfect square" using logical connectives.

CHOICES:

A. p v -q

B. p -> -q

C. p -q

D. p <-> -q

QUESTION 12:

Which of the following conditional statements is/are equivalent to. "If it rains, then I will not go to park".

i. If I will go to park, then it does not rain.

ii. If I will not go to park, then it rains.

iii. If it will not rain, then I go to park.

CHOICES:

A. i only

B. iii only

C. ii only

D. i, ii, and iii

QUESTION 13:

Which of the following conditional statements is/are counterexample/s to the statement: "If it is not a square, then it does not have four sides".

i. a rhombus

ii. a trapezoid

iii. a rectangle

CHOICES:

A. i only

B. iii only

C. ii only

D. i, ii, and iii

QUESTION 14:

Which of the following statement is the contrapositive form of the conditional statement, "If two numbers are odd, then their product is even."

CHOICES:

A. If the product of two numbers is even, then the two numbers are odd.

B. If the product of two numbers is odd, then the two numbers are even.

C. If two numbers are even, then their product is odd.

D. If two numbers are even, then their product is even.

QUESTION 15:

How many propositions are there in the argument below?

If horses fly or cows eat artichokes, then the mosquito is the national bird.

If the mosquito is the national bird, then peanut butter tastes good in hotdogs.

But peanut butter tastes terrible on hotdogs.

Therefore, cows don't eat artichokes.

CHOICES:

A. 2

B. 4

C. 3

D. 5

QUESTION 16:

If p - > q is a false statement, which of the following statements are true?

i. (p v q) p

ii. -p -q

iii. q p

CHOICES:

A. i and ii

B. ii and iii

C. i and iii

D. i, ii and iii

QUESTION 17:

Consider the argument:

Premise 1: (p q v q) p

Premise 2: -r -q

Premise 3: q v r p

Conclusion: r

Write the above argument in its symbolic statement form.

CHOICES:

A. {[(p q -r) (q v r)]} r

B. {p [(q -r) (q v r)] r}

C. {(p q) [(-r q) v r]} r

D. {[(p q) -r] (q v r)} r

QUESTION 18:

Consider the conditional statement, "If 3 is not an even integer, then the square root of 4 is even". Which type of transformation of the conditional statement is the statement, "If 3 is an even integer, then the square root of 4 is not even"?

CHOICES:

A. Inverse

B. Contrapositive

C. Converse

D. Contradiction

QUESTION 19:

How much interest was earned by an investment that earns at a rate of 9% compounded semi-annually for 7 years if the initial investment is at 18,000.00?

CHOICES:

A. 15,335.01

B. 15,353.01

C. 15,535.01

D. 15,533.01

QUESTION 20:

Geian went to the mall to shop. He went to a store, spent half of his money and then 500 more. He went to a second store, he spent half of his remaining money and then 500 more. He then had no money left. How much did he have to begin with when he went to the first store?

CHOICES:

A. Finding a pattern

B. Formulation of an Equation using a Variable

C. Solving a Similar but a Simpler Problem

D. Working Backwards

QUESTION 21:

Consider the argument:

Premise 1: p v -q

Premise 2: -q

Premise 3: p

Conclusion: r

Which truth values of p and q is the argument, written as a conditional, true?

i. p is false; q is true

ii. p is true; q is false

iii. p is true; q is true

CHOICES:

A. i only

B. iii only

C. ii only

D. i, ii, and iii

QUESTION 22:

Which of the following are well formed symbolic propositional statements?

i: - [p (q p)]

ii: - [p - (q p)]

iii: (p -q) v ( q -p)

CHOICES:

A. i and ii only

B. ii and iii only

C. i and iii only

D. i, ii, and iii