turkey-yks 2013 Q12

turkey-yks · Other · lys1-math Number Theory Algebraic Structures in Number Theory
An operation $\Theta$ is defined on the set of integers for every integers a and b as
$$a \ominus b = a - b + 1$$
Regarding the $\Theta$ operation, I. The identity element is 1. II. It has the commutative property. III. It has the associative property. Which of these statements are true?
A) Only I
B) I and II
C) I and III
D) II and III
E) I, II and III 
An operation $\Theta$ is defined on the set of integers for every integers a and b as

$$a \ominus b = a - b + 1$$

Regarding the $\Theta$ operation,\\
I. The identity element is 1.\\
II. It has the commutative property.\\
III. It has the associative property.\\
Which of these statements are true?\\
A) Only I\\
B) I and II\\
C) I and III\\
D) II and III\\
E) I, II and III
Paper Questions
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