Practice Problems on Sets

Which of the following is NOT a set?

• collection of real numbers greater than 78

• collection of brave students in Math 10

• collection of professors in DPSM who are taller than Prof. Chavez

• collection of Hermes bags in Heart Evangelista’s closet

Which of the following is FALSE?

• Any set is a subset of itself.

Which of the following sets is not equal to the rest of the choices?

• {a, e, l, m, n, t}

• {z | z is a distinct letter in the word  “lament”}

• {x | x is a distinct letter in the word  “menial”}

• { y | y is a distinct letter in the word  “elemental”}

Which of the following is TRUE?

• The set of even numbers is equivalent to the set of rational numbers.

• The cardinality of the set of real numbers is aleph-null.

Given the following sets:

N = set of natural numbers,

Q = set of rational numbers,

R = set of real numbers,

W = set of whole numbers,

Z = set of integers,

Which of the following is the correct order of the following sets of numbers in increasing order (Smallest set to largest set).

• R, Q, W, Z, N

• N, Q, R, W, Z

• N, W, Z, Q, R

• R, Q, Z, W, N

• 
• 
• 
• 

• {x | x is a whole number between 5 and 6}

• {x | x is an odd number between 7 and 11}

• {x | x is a vowel in the word "rhythm"}

• {x | x is a prime number between 7 and 11}

• S and T are disjoint

Write the following in roster method:

M = set of prime numbers between 0 and 10

• {1, 2, 3, 5, 7, 9}

• {2, 3, 5, 7}

• {2, 3, 5, 7, 9}

• {1, 3, 5, 7, 9}

Answer explanation

1 is neither prime nor composite and 9 is not prime since its divisible by 3.

• { g }

• { j }

• { j, k }

• { d, e, f, j, k }

• none of the choices