Sets in Number Theory

Which set represents the set of positive natural numbers?

• N = {0, 1, 2, 3, 4, ...}

• Z = {..., -3, -2, -1, 0, 1, 2, 3, ...}

• N+ = {1, 2, 3, 4, ...}

• Q = { m/n | m ∈ Z, n ∈ N+ }

What does the set N represent in number theory?

• Set of positive natural numbers

• Set of whole numbers (integers)

• Set of natural numbers

• Set of rational numbers

Which set is defined as the set of whole numbers (integers)?

• N+

• N

• Z

• Q

What is the set Q composed of?

• Rational and irrational numbers

• Positive natural numbers

• Rational numbers

• Natural numbers

Which set includes both rational and irrational numbers?

• N+

• Q

• Z

• R

What does the set C represent?

• Set of natural numbers

• Set of complex numbers

• Set of rational numbers

• Set of whole numbers

What is the definition of divisibility in the context of integers?

• A) A number b divides a number a if a is a multiple of b and b is not zero.

• B) A number b divides a number a if a is a sum of b and b is not zero.

• C) A number b divides a number a if a is a difference of b and b is not zero.

• D) A number b divides a number a if a is a division of b and b is not zero.

Which of the following statements is true according to the divisibility rule?

• A) b | a means that the remainder following division by b is not zero.

• B) b | a means that the remainder following division by b is zero.

• C) b | a means that the remainder following division by b is one.

• D) b | a means that the remainder following division by b is b.

Based on the example given, which statement is correct?

• A) 5 divides 10 since 10 = 2 × 5.

• B) 10 divides 5 since 5 = 2 × 10.

• C) 5 divides 11 since 11 = 2 × 5.

• D) 11 divides 5 since 5 = 2 × 11.

Why does 10 not divide 5 according to the example?

• A) Because 5 is a multiple of 10.

• B) Because 5 = 1/2 × 10 and 1/2 is not an integer.

• C) Because 10 is not an integer.

• D) Because the remainder when dividing 5 by 10 is 5.