Question:
Subtraction of integers is:
- (a) Commutative but not associative
- (b) Commutative and associative
- (c) Associative but not commutative
- (d) Neither commutative nor associative
Solution:
Step 1: Check Commutativity
\[ a – b \neq b – a \]
Example:
\[ 5 – 3 = 2 \neq -2 = 3 – 5 \]
So, subtraction is not commutative.
—Step 2: Check Associativity
\[ (a – b) – c \neq a – (b – c) \]
Example:
\[ (5 – 3) – 2 = 2 – 2 = 0 \]
\[ 5 – (3 – 2) = 5 – 1 = 4 \]
So, subtraction is not associative.
—Final Answer:
\[ \boxed{\text{(d) Neither commutative nor associative}} \]