Mth202 Quiz 2 Fall 2024

Here are all the MCQs and their correct answers for your MTH202 - Discrete Mathematics (Quiz No. 2):

1. If $f(x) = \sin^{-1}(x)$ and $g(x) = \sin(x)$, then $g \circ f(x)$ is:

   • Answer: x

2. Input values of the function are called the:

   • Answer: Domain

3. A relation $R$ is said to be _______ iff it is reflexive, antisymmetric, and transitive.

   • Answer: Partial order Relation

4. If $f: \mathbb{Z} \to \mathbb{R}$ and $g: \mathbb{R} \to \mathbb{R}$ are both onto functions, then $g \circ f: \mathbb{Z} \to \mathbb{R}$ is:

   • Answer: onto

5. Why is the function $f(x) = \frac{1}{x^2 - 25}$ not well defined?

   • Answer: Because $f$ is not defined for 5 and -5.

6. Let $f(x) = 2x$ and $g(x) = x + 2$, then $(f - g)(x)$ is:

   • Answer: $x - 2$

7. Cardinality of positive prime numbers less than 20 is:

   • Answer: 8

8. Inverse of a surjective function is always a function.

   • Answer: False

9. Number of one-to-one functions from $X = \{a, b\}$ to $Y = \{u, v\}$ is:

   • Answer: 2

10. Let $C$ be the set of all countries in the world. Then $C$ is a:

• Answer: Finite set

Good luck! Let me know if you need further clarification on any of the answers.