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Easy

Question

Let $Z$ denote the set of integers, then
$open curly brackets x element of Z colon open vertical bar x minus 3 close vertical bar less than 4 close curly brackets n open curly brackets x element of Z colon open vertical bar x minus 4 close vertical bar less than 5 close curly brackets equals$

${- 1,0, 1,2, 3,4}$
$\{- 1,0, 1,2, 3,4, 5\}$
${0,1, 2,3, 4,5, 6}$
${- 1,0, 1,2, 3,5, 6,7, 8,9}$

The correct answer is: $left curly bracket 01 comma 23 comma 45 comma 6 right curly bracket$

We have,
$open curly brackets x element of Z colon open vertical bar x minus 3 close vertical bar less than 4 close curly brackets equals open curly brackets x element of Z colon negative 1 less than x less than 7 close curly brackets equals left curly bracket 01 comma 23 comma 45 comma 6 right curly bracket$
and,
$open curly brackets x element of Z colon open vertical bar x minus 4 close vertical bar less than 5 close curly brackets equals open curly brackets x element of Z colon negative 1 less than x less than 9 close curly brackets$
$equals left curly bracket 01 comma 23 comma 45 comma 67 comma 8 right curly bracket$
$therefore open curly brackets x element of Z colon open vertical bar x minus 3 close vertical bar less than 4 close curly brackets intersection left curly bracket x element of Z colon open vertical bar x minus 4 close vertical bar less than 5 right curly bracket$
$equals open curly brackets 01 comma 23 comma 45 comma 6 close curly brackets$

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