MATH-105
Contemporary Mathematics
FINAL READINESS EXAM
Q&S
©2024/2025
, 1. Question: In the context of group theory, which of the
following sets along with the operation given forms a group?
- A. The set of all integers with addition.
- B. The set of all positive integers with multiplication.
- C. The set of non-zero rational numbers with
multiplication.
- D. The set of all real numbers excluding zero with
multiplication.
Answer: C. The set of non-zero rational numbers with
multiplication.
Rationale: This set forms a group because it satisfies
all group properties: closure, associativity, identity (1), and
inverses (e.g., for any rational number `a/b`, its inverse is
`b/a`).
2. Question: Which of the following sequences converges
to zero as \( n \to \infty \)?
- A. \( a_n = \frac{1}{n} \)
- B. \( b_n = \frac{n}{n+1} \)
- C. \( c_n = (-1)^n \)
- D. \( d_n = \sin(n) \)
Answer: A. \( a_n = \frac{1}{n} \)
Rationale: As \( n \to \infty \), \(\frac{1}{n} \to 0\). The
other sequences either oscillate or converge to values other
than zero.
3. Question: Which type of infinity is larger in the context
of set theory?
- A. The cardinality of the set of natural numbers.
- B. The cardinality of the set of real numbers.
©2024/2025
Contemporary Mathematics
FINAL READINESS EXAM
Q&S
©2024/2025
, 1. Question: In the context of group theory, which of the
following sets along with the operation given forms a group?
- A. The set of all integers with addition.
- B. The set of all positive integers with multiplication.
- C. The set of non-zero rational numbers with
multiplication.
- D. The set of all real numbers excluding zero with
multiplication.
Answer: C. The set of non-zero rational numbers with
multiplication.
Rationale: This set forms a group because it satisfies
all group properties: closure, associativity, identity (1), and
inverses (e.g., for any rational number `a/b`, its inverse is
`b/a`).
2. Question: Which of the following sequences converges
to zero as \( n \to \infty \)?
- A. \( a_n = \frac{1}{n} \)
- B. \( b_n = \frac{n}{n+1} \)
- C. \( c_n = (-1)^n \)
- D. \( d_n = \sin(n) \)
Answer: A. \( a_n = \frac{1}{n} \)
Rationale: As \( n \to \infty \), \(\frac{1}{n} \to 0\). The
other sequences either oscillate or converge to values other
than zero.
3. Question: Which type of infinity is larger in the context
of set theory?
- A. The cardinality of the set of natural numbers.
- B. The cardinality of the set of real numbers.
©2024/2025
