If V = {x : x ∈ Z and |x| < 3}, what is V?यदि V = {x : x ∈ Z और |x| < 3}, तो V क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: V = {-2, -1, 0, 1, 2}V = {-2, -1, 0, 1, 2}
For an integer x, the condition |x| < 3 means that x is fewer than three units from zero. It is equivalent to −3 < x < 3. The integers strictly between these endpoints are −2, −1, 0, 1 and 2, so V = {−2, −1, 0, 1, 2}. The endpoints −3 and 3 are excluded because the inequality is strict, and zero is included because |0| = 0.पूर्णांक x के लिए |x| < 3 का अर्थ है कि शून्य से x की दूरी 3 से कम है। इसे −3 < x < 3 के रूप में लिखा जा सकता है। इन सीमाओं के बीच आने वाले पूर्णांक −2, −1, 0, 1 और 2 हैं, इसलिए V = {−2, −1, 0, 1, 2}। −3 और 3 शामिल नहीं हैं, क्योंकि असमानता सख्त है। 0 अवश्य शामिल है, क्योंकि |0| = 0 < 3।
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