Binary Operation

Question 1

T or F

If * is any binary operation on any set S, then a*a=a for all a is an element of S.

Answer 1

F

Question 2

If * is any commutative binary operation on any set S, then a(bc)=(bc)a for all a, b, c is an element of S.

Answer 2

T

Question 3

If * is any associative binary operation on any set S, then a(bc)=(bc)a for all a, b, c is an element of S.

Answer 3

F

Question 4

The only binary operations of any importance are those defined on sets of numbers.

Answer 4

F

Question 5

A binary operation * on a set S is commutative if there exist a, b is an element of S such that ab=ba

Answer 5

F

Question 6

A binary operation on a set S assigns at least one element of S to each ordered pair of elements of S.

Answer 6

T

Question 7

A binary operation on a set S assigns at most one element of S to each ordered pair of elements of S.

Answer 7

T

Question 8

A binary operation on a set S assigns exactly one element of S to each ordered pair of elements of S.

Answer 8

T

Question 9

Every binary operation defined on a set having exactly one element is both commutative and associative.

Answer 9

F

Question 10

A binary operation on a set S may assign more than one element of S to some ordered pair of elements of S.

Answer 10

F