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Representations of Organic Compounds

Define:a Ele...

Question

Define:

(a) Elements

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Solution

An element is defined as a pure substance made up of only one kind of atoms. An element cannot be broken down into simpler substances by chemical reactions.

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For each binary operation * defined below, determine whether * is commutative or associative.

(i) On Z, define a * b = a − b

(ii) On Q, define a * b = ab + 1

(iii) On Q, define a * b

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For each binary operation $*$ defined below, determine whether $*$ is binary, commutative or associative.
(i) On Z, define a $*$ b =a-b

(ii) On Q, define $a * b = a b + 1$

(iii) On Q, define $a * b = \frac{a b}{2}$

(iv) On $Z^{+}$ , define $a * b = 2^{a b}$

(v) On $Z^{+}$ , define $a * b = a^{b}$

(vi) On (R-{-1} ,define $a * b = \frac{a}{b + 1}$

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