MathDB

2

Part of 1979 VTRMC

Problems(1)

VTRMC 1979 #2

Source:

8/8/2018
Let SS be a set which is closed under the binary operation ∘\circ, with the following properties: (i) there is an element e∈Se \in S such that a∘e=e∘a=aa \circ e = e \circ a = a, for each a∈Sa \in S. (ii) (a∘b)∘(c∘d)=(a∘c)∘(b∘d)(a \circ b) \circ (c \circ d)=(a \circ c) \circ (b \circ d), for all a,b,c,d∈Sa,b, c,d \in S.
Prove or disprove: (a) ∘\circ is associative on S (b) ∘\circ is commutative on S
Sets