Muft Shiksha
Update

Muft Shiksha™ एक 100% Free Education Portal है 🇮🇳, जिसका उद्देश्य Class 9–12 के हर विद्यार्थी तक High-Quality Education को पूरी तरह मुफ्त पहुँचाना है। 🇮🇳 हम मानते हैं कि अच्छी शिक्षा किसी student की आर्थिक स्थिति पर निर्भर नहीं होनी चाहिए। 🇮🇳 हर विद्यार्थी को वही Quality Study Material, MCQs, Quizzes, Exam Preparation, Concept-Based Learning और Bilingual Support मिलना चाहिए, जो आमतौर पर महंगी Coaching या Premium Platforms में मिलता है। Muft Shiksha™ 🇮🇳 इसी सोच के साथ बनाया गया है

Subjects
Class 10MathematicsSetsThe Empty Set, Finite and Infinite Sets, Equal SetsEasyLevel 4

If Z = {x : x ∈ ℤ, x² ≤ 4}, how many elements does Z have?

Advertisement

Answer and explanation

Correct answer: 5

The inequality x² ≤ 4 is equivalent to |x| ≤ 2, so −2 ≤ x ≤ 2. The integers in this closed interval are −2, −1, 0, 1, and 2. Therefore Z = {−2, −1, 0, 1, 2}, which has five elements. Unlike a strict inequality, ≤ includes both boundary values −2 and 2.

Tags

setsfinite setintegerssquare inequalityThe Empty SetFinite and Infinite SetsEqual Setsthe empty set finite and infinite sets equal setsMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

5

Why is this the correct answer?

The inequality x² ≤ 4 is equivalent to |x| ≤ 2, so −2 ≤ x ≤ 2. The integers in this closed interval are −2, −1, 0, 1, and 2. Therefore Z = {−2, −1, 0, 1, 2}, which has five elements. Unlike a strict inequality, ≤ includes both boundary values −2 and 2.

Which subject and chapter does this question cover?

This is a Class 10 Mathematics question. Chapter: Sets. Topic: The Empty Set, Finite and Infinite Sets, Equal Sets.

Report question
Advertisement