Question

Let k be a nonempty subset of a field F Then K is a subfield of F​

Answer 1

SOLUTION

TO CHECK

True / False below statement :

Let k be a nonempty subset of a field F Then K is a subfield of F

EVALUATION

A non empty subset K of a field F is said to be a subfield of F if the elements of K form a field with respect to the compositions of F restricted to K

More precisely , Let F be a field . A non empty subset K of a field F is said to be a subfield of F if and only if

$\sf{(i) \: \: a \in K , b \in K \: \implies \: a - b \in K}$

$\sf{(ii) \: \: a \in K , 0 \ne b \in K \: \implies \: a {b}^{ - 1} \in K}$

Hence the given statement is FALSE

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