Quiz for Sets, Relations, Functions

Q1: If A = {1, 2, 3} and B = {2, 3, 4}, then A ∩ B is?

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

Q2: What is the number of subsets of a set with n elements?

A. n B. n² C. 2^n D. n!

Q3: If f(x) = x², then f(-x) equals?

A. x B. x² C. -x² D. -x

Q4: Which of the following is a function?

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

Q5: The domain of the function f(x) = 1/(x−2) is?

A. x ≠ 2 B. x ≠ 0 C. x > 2 D. All real numbers

Q6: If f(x) = x + 3 and g(x) = 2x, then f∘g(x) is?

A. 2x + 3 B. 2x + 6 C. x + 6 D. 6x + 3

Q7: Let A = {1, 2, 3}, the number of binary relations on A is?

A. 9 B. 81 C. 27 D. 64

Q8: A function f: R → R is said to be even if?

A. f(-x) = -f(x) B. f(x) = f(-x) C. f(x) = x D. f(x) = -x

Q9: What is the range of the function f(x) = |x|?

A. All real numbers B. x ≥ 0 C. x > 0 D. x ≤ 0

Q10: If A has m elements and B has n elements, number of functions from A to B is?

A. m^n B. n^m C. m+n D. m*n

Q11: A function is said to be onto (surjective) if?

A. Every element of codomain has a preimage B. One-to-one C. f(x) = x D. Injective only

Q12: The inverse of f(x) = 3x + 2 is?

A. (x−2)/3 B. (x+2)/3 C. 3x−2 D. x/3 + 2

Q13: Which is not a valid function definition?

A. f: R → R, f(x) = 1/x B. f: R → R, f(x) = √x C. f: R → R, f(x) = |x| D. f: R → R, f(x) = x²

Q14: A set that contains no elements is called?

A. Universal Set B. Singleton C. Null Set D. Finite Set

Q15: If A ⊆ B, then A ∩ B = ?

A. A B. B C. A ∪ B D. ∅

Q16: If f(x) = 1/(x²+1), then the range is?

A. (0, ∞) B. (1, ∞) C. [0, ∞) D. (0, 1]

Q17: Function f(x) = ln(x) is defined for?

A. x > 0 B. x ≥ 0 C. x < 0 D. All real x

Q18: If A = {1,2}, B = {a,b}, then total number of one-to-one functions from A to B is?

A. 2 B. 4 C. 0 D. 1

Q19: Which of these is an identity function?

A. f(x) = x B. f(x) = x² C. f(x) = 1/x D. f(x) = |x|

Q20: The power set of set A = {1, 2} is?

A. {{1}, {2}} B. {{∅}, {1,2}} C. {{∅}, {1}, {2}, {1,2}} D. {{1,2}, {2}}