Consider the binary operations*: R x R and o :R x R defined as a ⋅ b=∣a−b∣ and aob=afor all a, b ∈R˙Show that * is commutative but not associative, ′o′is associative but not commutative.

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Consider the binary operations*: {R} {x} {R}{ }and {o} :{R} {x

Question

Consider the binary operations: $R x R$ and $o : R x R$ defined as a $\cdot b = ∣ a - b ∣$ and $a o b = a$ for all $a, b \in R ˙$ Show that is commutative but not associative, $^{'} o^{'}$ is associative but not commutative.

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Samuel Discussed

Consider the binary operations*:

R x R

and

o : R x R

defined as a

\cdot b = ∣ a - b ∣

and

a o b = a

for all

a, b \in R ˙

Show that * is commutative but not associative,

^{'} o^{'}

is associative but not commutative.

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Question Text

Consider the binary operations*:

R x R

and

o : R x R

defined as a

\cdot b = ∣ a - b ∣

and

a o b = a

for all

a, b \in R ˙

Show that * is commutative but not associative,

^{'} o^{'}

is associative but not commutative.