Practice Multiplication Modulo K (13.5) - Group Theory - Discrete Mathematics

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8 questions

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6 sample questions

Question 1.
What is the identity element in multiplication modulo 7?
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Think about what number keeps others unchanged when you multiply.
Question 2.
List the co-prime integers with respect to 4.
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Consider what numbers have no common factors with 4.
3Question 3.
What is a group?
- A set with one operation
- A collection of elements that satisfies certain properties
- A number line
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Recall the definition of a group we discussed.
4Question 4.
True or False: The identity element in multiplication modulo k is always 0.
- True
- False
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Think about what multiplying any number by 0 results in.
Question 5.
Prove that if a and b are in ℤ* for some k, then the inverse of their product in multiplication modulo k is the product of their inverses.
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Use the definition of inverses in group theory.
Question 6.
Given k as a prime number, explain how ℤ* under multiplication modulo k simplifies to the entire non-zero set of integers less than k.
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Utilize the property of primes in relation to factors.

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