We say a binary operation ∗ is associative when a ∗ (b ∗ c) = (a ∗ b) ∗ (a ∗c)
True
False
We say a binary operation ∗ is associative if a ∗ (b ∗ c) = (a ∗ b) ∗ c. So the given statement is false.
Consider the binary operations*: R ×R → and o: R × R → R defined as and a o b = a, &mnForE;a, b ∈ R. Show that * is commutative but not associative, o is associative but not commutative. Further, show that &mnForE;a, b, c ∈ R, a*(b o c) = (a * b) o (a * c). [If it is so, we say that the operation * distributes over the operation o]. Does o distribute over *? Justify your answer.