Sets & Relations: Essential Concepts for Competitive Exams

Sets & Relations

Q. How many subsets can be formed from the set S = {a, b, c, d}?

A. 4
B. 8
C. 16
D. 2

Solution

The number of subsets of a set with n elements is 2^n. Here, n = 4, so the number of subsets is 2^4 = 16.

Correct Answer: B — 8

Learn More →

Q. How many subsets does the set A = {a, b, c} have?

A. 2
B. 3
C. 4
D. 8

Solution

The number of subsets of a set with n elements is 2^n. Here, n = 3, so the number of subsets is 2^3 = 8.

Correct Answer: D — 8

Learn More →

Q. How many subsets does the set {a, b, c} have?

A. 2
B. 3
C. 4
D. 8

Solution

The number of subsets of a set with n elements is 2^n. Here, n = 3, so the number of subsets is 2^3 = 8.

Correct Answer: D — 8

Learn More →

Q. If A = {1, 2, 3, 4} and B = {2, 4, 6, 8}, what is A ∪ B?

A. {1, 2, 3, 4, 6, 8}
B. {2, 4}
C. {1, 3, 5, 7}
D. {1, 2, 3, 4, 5}

Solution

The union A ∪ B includes all elements from both sets, which are {1, 2, 3, 4, 6, 8}.

Correct Answer: A — {1, 2, 3, 4, 6, 8}

Learn More →

Q. If A = {1, 2, 3} and B = {1, 2, 3, 4, 5}, what is A ⊆ B?

A. True
B. False
C. Depends on the context
D. None of the above

Solution

Set A is a subset of set B because all elements of A are contained in B. Therefore, A ⊆ B is True.

Correct Answer: A — True

Learn More →

Q. If A = {1, 2, 3} and B = {1, 2, 3, 4}, what is the cardinality of A × B?

A. 3
B. 6
C. 9
D. 12

Solution

The cardinality of the Cartesian product A × B is given by |A| * |B|. Here, |A| = 3 and |B| = 4, so |A × B| = 3 * 4 = 12.

Correct Answer: B — 6

Learn More →

Q. If A = {1, 2, 3} and B = {1, 2, 3}, what is A × B?

A. {(1,1), (2,2), (3,3)}
B. {(1,2), (2,3), (3,1)}
C. {(1,1), (1,2), (1,3), (2,1), (2,2), (2,3), (3,1), (3,2), (3,3)}
D. {}

Solution

A × B = {(1,1), (1,2), (1,3), (2,1), (2,2), (2,3), (3,1), (3,2), (3,3)} as it is the Cartesian product of A and B.

Correct Answer: C — {(1,1), (1,2), (1,3), (2,1), (2,2), (2,3), (3,1), (3,2), (3,3)}

Learn More →

Q. If A = {1, 2, 3} and B = {3, 4, 5}, what is A - B?

A. {1, 2}
B. {3}
C. {4, 5}
D. {1, 2, 3, 4, 5}

Solution

The difference of sets A and B, A - B, contains elements that are in A but not in B. Here, A - B = {1, 2}.

Correct Answer: A — {1, 2}

Learn More →

Q. If A = {1, 2, 3} and B = {3, 4, 5}, what is A Δ B (symmetric difference)?

A. {1, 2}
B. {4, 5}
C. {1, 2, 4, 5}
D. {3}

Solution

The symmetric difference A Δ B includes elements in either A or B but not in both, which are {1, 2, 4, 5}.

Correct Answer: C — {1, 2, 4, 5}

Learn More →

Q. If A = {1, 2, 3} and B = {3, 4, 5}, what is A ∪ (A ∩ B)?

A. {1, 2, 3}
B. {3, 4, 5}
C. {1, 2, 3, 4, 5}
D. {1, 2, 5}

Solution

First, A ∩ B = {3}. Then, A ∪ {3} = {1, 2, 3}.

Correct Answer: A — {1, 2, 3}

Learn More →

Q. If A = {x | x is a letter in the word 'MATH'} and B = {x | x is a letter in the word 'SCIENCE'}, what is A ∩ B?

A. {A}
B. {M, A, T}
C. {A, C, E}
D. {A, T}

Solution

The intersection A ∩ B includes letters that are common in both words. The only common letter is 'A', so A ∩ B = {A}.

Correct Answer: A — {A}

Learn More →

Q. If A = {x | x is a letter in the word 'MATH'} and B = {x | x is a letter in the word 'SET'}, what is A ∩ B?

A. {M, A, T}
B. {A, T}
C. {T}
D. {}

Solution

The intersection A ∩ B consists of common letters, which is {T}.

Correct Answer: C — {T}

Learn More →

Q. If A = {x | x is a multiple of 3} and B = {x | x is a multiple of 5}, what is A ∩ B?

A. {15}
B. {3, 5}
C. {0}
D. {}

Solution

The intersection A ∩ B consists of common multiples, which is {0}.

Correct Answer: C — {0}

Learn More →

Q. If A = {x | x is a natural number and x < 5} and B = {x | x is a natural number and x > 2}, what is A ∩ B?

A. {1, 2}
B. {3, 4}
C. {2, 3, 4}
D. {1, 2, 3, 4}

Solution

Set A = {1, 2, 3, 4} and set B = {3, 4, 5, ...}. The intersection A ∩ B = {3, 4}.

Correct Answer: B — {3, 4}

Learn More →

Q. If A = {x | x is a natural number less than 5} and B = {x | x is a natural number less than 3}, what is A - B?

A. {1, 2}
B. {3, 4}
C. {1, 2, 3, 4}
D. {2, 3, 4}

Solution

Set A = {1, 2, 3, 4} and set B = {1, 2}. Thus, A - B = {3, 4}.

Correct Answer: B — {3, 4}

Learn More →

Q. If A = {x | x is a natural number less than 5} and B = {x | x is an odd natural number}, what is A ∩ B?

A. {1, 2, 3, 4}
B. {1, 3}
C. {2, 4}
D. {1, 2, 3}

Solution

The intersection A ∩ B includes elements that are in both A and B. Here, A = {1, 2, 3, 4} and B = {1, 3}, so A ∩ B = {1, 3}.

Correct Answer: B — {1, 3}

Learn More →

Q. If A = {x | x is a prime number less than 10} and B = {2, 3, 5, 7}, what is A = B?

A. True
B. False
C. Cannot be determined
D. None of the above

Solution

Both sets A and B contain the same elements: {2, 3, 5, 7}. Therefore, A = B is True.

Correct Answer: A — True

Learn More →

Q. If A = {x | x is a prime number less than 10} and B = {2, 3, 5, 7}, what is A?

A. {2, 3, 5, 7}
B. {1, 2, 3, 4, 5, 6, 7, 8, 9}
C. {2, 3, 5, 7, 11}
D. {2, 3, 5, 7, 9}

Solution

The set A consists of all prime numbers less than 10, which are {2, 3, 5, 7}.

Correct Answer: A — {2, 3, 5, 7}

Learn More →

Q. If A = {x | x is a vowel} and B = {x | x is a consonant}, what is A ∩ B?

A. {a, e, i, o, u}
B. {}
C. {a, b, c}
D. {a, e, i}

Solution

The intersection A ∩ B is empty because no letter can be both a vowel and a consonant.

Correct Answer: B — {}

Learn More →

Q. If A = {x | x is an even integer} and B = {x | x is a multiple of 3}, what is A ∪ B?

A. {0, 2, 4, 6, ...}
B. {0, 3, 6, 9, ...}
C. {0, 2, 3, 4, 6, 9, ...}
D. {0, 2, 3, 4, 6, 8, 9, ...}

Solution

The union of sets A and B, A ∪ B, includes all even integers and all multiples of 3. Thus, A ∪ B = {0, 2, 3, 4, 6, 9, ...}.

Correct Answer: C — {0, 2, 3, 4, 6, 9, ...}

Learn More →

Q. If A = {x | x is an even integer} and B = {x | x is a prime number}, what is A ∩ B?

A. {2}
B. {2, 3}
C. {2, 4}
D. {}

Solution

The only even prime number is 2, so A ∩ B = {2}.

Correct Answer: A — {2}

Learn More →

Q. If A = {x | x is an even number} and B = {x | x is a prime number}, what is A ∩ B?

A. {2}
B. {2, 3}
C. {2, 4}
D. {}

Solution

A ∩ B = {2} as 2 is the only even prime number.

Correct Answer: A — {2}

Learn More →

Q. If R is a relation on set A = {1, 2, 3} defined by R = {(1, 1), (2, 2), (3, 3)}, is R symmetric?

A. Yes
B. No
C. Depends on A
D. None of the above

Solution

A relation is symmetric if for every (a, b) in R, (b, a) is also in R. Since R only contains pairs of the form (a, a), it is symmetric.

Correct Answer: A — Yes

Learn More →

Q. If the relation R on set A = {1, 2, 3} is defined as R = {(1, 2), (2, 3)}, is R reflexive?

A. Yes
B. No
C. Depends on A
D. None of the above

Solution

A relation is reflexive if every element is related to itself. Here, (1,1), (2,2), and (3,3) are not in R, so R is not reflexive.

Correct Answer: B — No

Learn More →

Q. If the universal set U = {1, 2, 3, 4, 5} and A = {1, 2}, what is A'?

A. {3, 4, 5}
B. {1, 2}
C. {1, 2, 3}
D. {2, 3, 4, 5}

Solution

The complement of A, denoted A', includes all elements in U that are not in A. Thus, A' = {3, 4, 5}.

Correct Answer: A — {3, 4, 5}

Learn More →

Q. If U = {1, 2, 3, 4, 5}, A = {1, 2}, and B = {2, 3}, what is A ∪ B?

A. {1, 2}
B. {1, 2, 3}
C. {1, 2, 3, 4, 5}
D. {2, 3, 4, 5}

Solution

The union A ∪ B includes all elements from both sets, which are {1, 2, 3}.

Correct Answer: B — {1, 2, 3}

Learn More →

Showing 1 to 26 of 26 (1 Pages)

Sets & Relations

On a scale of 0–10, how likely are you to recommend The Soulshift Academy?