Mth104 Quiz 2 Fall 2024

Here are all the quiz questions and their answers:

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Question 1

If $f(x) = x$ and $g(x) = |x|$, then $(f \circ g)(-4.5)$ is ________________.

Answer:
4.5

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Question 2

What is recursion in mathematics?

Answer:
A function that calls itself

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Question 3

Let $S$ be a nonempty set. A partition of $S$ is a subdivision of $S$ into overlapping, nonempty subsets.

Answer:
Given statement is false.

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Question 4

Let $R$ be a relation on a set $A$. Then:

Answer:
$R \cup R^{-1}$ is the symmetric closure of $R$.

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Question 5

If $f$ represents the identity function on set $A$, what is the image of element 3 under this function?

Answer:
3

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Question 6

A relation $R$ on a set $A$ is symmetric if whenever $a R b$ and $b R c$, then $a R c$, that is, if whenever $(a, b) \in R$, and $(b, c) \in R$, then $(a, c) \in R$.

Answer:
Given statement is false.

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Question 7

Determine when a relation $R$ on a set $A$ is not symmetric.

Answer:
There exists $(a, b) \in R$ such that $(b, a)$ does not belong to $R$.

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Question 8

The relation of equality on any set $S$ is an equivalence relation.

Answer:
Given statement is true.

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Question 9

For $f(x) = 2x - 3$ and $g(x) = x^2 - 1$, the composite function $(f \circ g)(x)$ is __________.

Answer:
$2x^2 - 5$

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Question 10

Let $m$ be a fixed positive integer. Two integers $a$ and $b$ are said to be congruent (modulo $m$) if $m$ divides $a - b$.

Answer:
Given statement is true.

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