Understanding Groups in Mathematics

Which of the following is NOT a requirement for a set to be considered a group?

• Associativity

• Identity element

• Thumb

• Closure

Why do the odd integers under addition fail to form a group?

• They do not have inverses.

• They do not have an identity element.

• They are not closed under addition.

• They lack associativity.

What is the identity element for the set of integers under addition?

• -1

• 0

• 1

• 2

Why do integers under multiplication not form a group?

• They lack closure.

• They lack an identity element.

• Zero does not have an inverse.

• They are not associative.

Why do multiples of seven under addition form a group?

• They lack an identity element.

• They are not closed under addition.

• They have inverses and are associative.

• They do not have inverses.