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Group axiom operation +,-,*,/ which satisfies R,C,W,Z,Q number system answer Why?

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Math Magician

1) All except W are groups under addition. In W, 1 has no additive inverse.

Senior Mathematics Faculty

All the set R, C, W, Z and Q satisfy all the axioms with respect to the operation + and * only. But only R and C satisfy all the group axioms with respect to the binary operation +,-,*,/ since only these two sets are closed wrt to the given operations.

Mathematics Teacher with 5 years experience

Because the operation satisfies the four axioms viz. closure law, associative law, identity and inverse so (R,+), (R,-), (R,*), (R,/) are all groups and (Z,+), (Z,-) are groups but(Z,*) is not a group because only -1&1 has inverse element


group axiom operation + satisfy R,C,W,Z,Q because this operation is unidirectinal

Mathematics Teacher

Z W, R, C,Q. form group on the operation +,

Mathematics Teacher



only addition and multiplication are satisfied by all these number systems

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