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
SubjectsMathematics
रिक्त समुच्चय, सीमित और असीमित समुच्चय, समान समुच्चय
In this Class 10 Mathematics topic from the chapter Sets, students learn how to identify and represent the empty set, which contains no elements, and distinguish finite sets from infinite sets by considering the number of elements they contain. The topic also explains equal sets, where two sets have exactly the same elements regardless of their order. Examples, symbols, and basic comparisons help students apply these ideas accurately.
Correct answer: A. (A ∩ B) ∪ (A ∩ C)
Explanation: This is the distributive law of intersection over union: A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C). An element belongs to the left side when it is in A and also in at least one of B or C. That means it is either in both A and B or in both A and C, which is exactly the right side. Hence option A is correct.
Correct answer: A. \(\varnothing\)
Explanation: The power set of any set contains the empty set. For the empty set itself, the power set is \(\mathcal{P}(\varnothing)=\{\varnothing\}\), which has exactly one element. Therefore, if \(\mathcal{P}(A\cap B)=\{\varnothing\}\), the original set must be empty. Hence, \(A\cap B=\varnothing\). Notice that \(\{\varnothing\}\) is a set containing the empty set, whereas \(\varnothing\) contains no elements.
Correct answer: C. 3
Explanation: Use each possible y from B and calculate x = 2y - 1. For y = 1, x = 1, giving (1,1); for y = 2, x = 3, giving (3,2); and for y = 3, x = 5, giving (5,3). All three calculated x-values belong to A, and every y-value belongs to B. Therefore, the valid ordered pairs are (1,1), (3,2), and (5,3), so their number is 3 and option C is correct.
Correct answer: B. 3
Explanation: Check each possible value of \(x\) from A. For \(x=0\), the equation becomes \(y^2=1\), so \(y=-1\) or \(y=1\), giving two pairs: \((0,-1)\) and \((0,1)\). For \(x=1\), \(y^2=0\), so \(y=0\), giving \((1,0)\). For \(x=2\), \(y^2=-3\), which is impossible. Thus there are three valid ordered pairs, so option B is correct.
