{"id":8384,"date":"2024-08-22T10:11:18","date_gmt":"2024-08-22T04:41:18","guid":{"rendered":"https:\/\/theexampillar.com\/ncert\/?p=8384"},"modified":"2024-08-22T10:11:18","modified_gmt":"2024-08-22T04:41:18","slug":"ncert-solutions-class-11-maths-chapter-2-relations-and-functions-ex-2-1","status":"publish","type":"post","link":"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-11-maths-chapter-2-relations-and-functions-ex-2-1\/","title":{"rendered":"NCERT Solutions Class 11 Maths Chapter 2 Relations and Functions – Ex 2.1"},"content":{"rendered":"

NCERT Solutions Class 11 Maths\u00a0<\/span><\/strong><\/span><\/h2>\n

The NCERT Solutions in English Language for Class 11 Mathematics Chapter – 2 Relations and Functions <\/strong>Exercise 2.1 has been provided here to help the students in solving the questions from this exercise.\u00a0<\/span><\/p>\n

Chapter 2 (Relations and Functions)\u00a0<\/span><\/strong><\/span><\/h2>\n\n\n\n
Exercise – 2.1<\/span><\/strong><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

 <\/p>\n

1. If \"NCER<\/strong>, find the values of\u00a0x<\/em>\u00a0and\u00a0y<\/em>.
\n<\/strong>Solution – <\/strong>We know that, <\/span>
\nIf two ordered pairs are equal, then their corresponding first elements and second elements are equal. <\/span>
\nWe are given that the pairs \"NCER , so the corresponding elements should also be equal. <\/span><\/p>\n

On solving both the equations, we get \u2013 <\/span>
\nx\/3 + 1 = 5\/3 \u00a0 \u00a0 and \u00a0 \u00a0y \u2013 2\/3 = 1\/3 <\/span>
\nx\/3 = 5\/3 \u2013 1 \u00a0 \u00a0and \u00a0 \u00a0y = 1\/3 + 2\/3 <\/span>
\nx\/3 = 2\/3 \u00a0 \u00a0and \u00a0 \u00a0y = 3\/3 <\/span>
\nx = 2 \u00a0 \u00a0and \u00a0 \u00a0y = 1 <\/span>
\nTherefore, x = 2 and y = 1<\/span><\/p>\n

2. If set A has 3 elements and set B = {3, 4, 5}, then find the number of elements in (A \u00d7 B).
\n<\/strong>Solution –\u00a0<\/strong>Given, number of elements of set A = 3 <\/span>
\nThe elements of set B are 3, 4, and 5. <\/span>
\nSo, number of elements of set B = 3 <\/span>
\nThen, number of elements in A\u00d7B = (Number of elements in A) \u00d7 (Number of elements in B) <\/span>
\n= 3 \u00d7 3 = 9 <\/span>
\nTherefore, the number of elements in (A \u00d7 B) will be 9. <\/span><\/p>\n

3. If G = {7, 8} and H = {5, 4, 2}, find G \u00d7 H and H \u00d7 G.
\n<\/strong>Solution – <\/strong>Given, G = {7, 8} and H = {5, 4, 2} <\/span>
\nThe cartesian product of two non-empty sets P \u00d7 Q is the set of all ordered pairs of elements from P and Q, i.e., <\/span>
\nP \u00d7 Q = {(p, q) : p \u2208 P, q \u2208 Q} <\/span>
\nSo, G \u00d7 H = {(7, 5), (7, 4), (7, 2), (8, 5), (8, 4), (8, 2)} and <\/span>
\nH \u00d7 G = {(5, 7), (5, 8), (4, 7), (4, 8), (2, 7), (2, 8)}\u00a0 <\/span><\/p>\n

4. State whether each of the following statements is true or false. If the statement is false, rewrite the given statement correctly.
\n<\/strong>(i) If P = {m<\/em>,\u00a0n<\/em>} and Q = {n<\/em>,\u00a0m<\/em>}, then P \u00d7 Q = {(m<\/em>,\u00a0n<\/em>), (n<\/em>,\u00a0m<\/em>)}
\nSolution –<\/strong>\u00a0The given statement is False.\u00a0 <\/span>
\nThe correct statement is: If P = {m, n} and Q = {n, m}, then P \u00d7 Q = { (m, m), n), (n, m), (n, n) }\u00a0<\/span><\/p>\n

(ii) If A and B are non-empty sets, then A \u00d7 B is a non-empty set of ordered pairs (x<\/em>,\u00a0y<\/em>) such that\u00a0x<\/em>\u00a0\u2208\u00a0A and\u00a0y<\/em>\u00a0\u2208\u00a0B.
\nSolution –<\/strong>\u00a0The given statement is true.<\/span><\/p>\n

(iii) If A = {1, 2}, B = {3, 4}, then A \u00d7 (B \u2229 \u03a6) = \u03a6
\n<\/strong>Solution –\u00a0<\/strong>The given statement is true. <\/span><\/p>\n

5. If A = {\u20131, 1}, find A \u00d7 A \u00d7 A.
\n<\/strong>Solution –\u00a0<\/strong>The A \u00d7 A \u00d7 A for a non-empty set A is given by
\nA \u00d7 A \u00d7 A = {(a, b, c) : a, b, c \u2208 A}, where (a, b, c) is called an ordered triplet <\/span>
\nHere, given A = {\u20131, 1}, <\/span>
\nSo, <\/span>
\nA \u00d7 A \u00d7 A \u00a0= {(-1, -1,-1), (-1, -1, 1), (-1, 1, -1), (-1, 1, 1), (1, -1, -1), (1,-1, 1), (1, 1,-1), (1, 1, 1)}<\/span><\/p>\n

6. If A \u00d7 B = {(a<\/em>,\u00a0x<\/em>), (a<\/em>,\u00a0y<\/em>), (b<\/em>,\u00a0x<\/em>), (b<\/em>,\u00a0y<\/em>)}. Find A and B.
\n<\/strong>Solution –\u00a0<\/strong>Given,
\nA \u00d7 B = {(a<\/em>,\u00a0x<\/em>), (a,<\/em>\u00a0y<\/em>), (b<\/em>,\u00a0x<\/em>), (b<\/em>,\u00a0y<\/em>)}
\nSince, the cartesian product of two non-empty sets P \u00d7 Q is given by \u2013 <\/span>
\nP \u00d7 Q = {(p, q) : p \u2208 P, q \u2208 Q} <\/span>
\nSo, A is the set of all first elements and B is the set of all second elements. <\/span>
\nTherefore, A = {a, b} and B = {x, y}\u00a0<\/span><\/p>\n

7. Let A = {1, 2}, B = {1, 2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8}. Verify that
\n<\/strong>(i) A \u00d7 (B \u2229 C) = (A \u00d7 B) \u2229 (A \u00d7 C)
\n<\/strong>(ii) A \u00d7 C is a subset of B \u00d7 D
\n<\/strong>Solution –\u00a0<\/strong>Given,
\nA = {1, 2},
\nB = {1, 2, 3, 4},
\nC = {5, 6} and
\nD = {5, 6, 7, 8} <\/span><\/p>\n

(i)<\/strong> To verify: A \u00d7 (B \u2229 C) = (A \u00d7 B) \u2229 (A \u00d7 C)<\/span>
\nSince B \u2229 C= {1,2, 3,4} \u2229 {5,6} = \u2205 <\/span>
\nThus, L.H.S.= A \u00d7 (B \u2229 C) = A \u00d7 \u2205 = \u2205<\/span>
\nNow,\u00a0 <\/span>
\nA x B = { (1, 1), (1, 2), (1, 3), (1, 4), (2, 1), (2, 2), (2, 3), (2, 4) }<\/span>
\nA x C = { (1, 5), (1, 6), (2, 5), (2, 6) }<\/span>
\nThus, R.H.S. = (A \u00d7 B) \u2229 (A \u00d7 C) = \u2205<\/span>
\nTherefore, L.H.S. = R.H.S <\/span>
\nHence, verified.<\/strong><\/span><\/p>\n

(ii) <\/strong>To verify: A \u00d7 C is a subset of B \u00d7 D <\/span>
\nHere, <\/span>
\nA \u00d7 C = {(1, 5), (1, 6), (2, 5), (2, 6)} <\/span>
\nB \u00d7 D = {(1, 5), (1, 6), (1, 7), (1, 8), (2, 5), (2, 6), (2, 7), (2, 8), (3, 5), (3, 6), (3, 7), (3, 8), (4, 5), (4, 6), (4, 7), (4, 8)} <\/span>
\nSince, all the elements of set A x C are the elements of set B \u00d7 D<\/span>
\nThus, A \u00d7 C is a subset of B \u00d7 D <\/span>
\nHence, verified.<\/strong><\/span><\/p>\n

8. Let A = {1, 2} and B = {3, 4}. Write A \u00d7 B. How many subsets will A \u00d7 B have? List them.
\n<\/strong>Solution –\u00a0<\/strong>Given, A = {1, 2} and B = {3, 4}
\nSo,
\nA \u00d7 B = {(1, 3), (1, 4), (2, 3), (2, 4)}
\nNumber of elements in A \u00d7 B is\u00a0n<\/em>(A \u00d7 B) = 4
\nWe know that,
\nIf C is a set with\u00a0n<\/em>(C) =\u00a0m<\/em>, then\u00a0n<\/em>[P(C)] = 2m<\/sup><\/em>.
\nThus, the set A \u00d7 B has 24<\/sup> = 16 subsets.
\nAnd these subsets are as given below:
\n\u2205, {(1, 3)}, {(1, 4)}, {(2, 3)}, {(2, 4)}, { (1, 3), (1, 4) }, { (1, 3), (2, 3) }, { (1, 3), (2, 4) }, {(1, 4), (2, 3)}, { (1, 4), (2, 4) }, { (2, 3), (2, 4) }, {(1, 3), (1, 4), (2, 3) }, { (1, 3), (1, 4), (2, 4) }, { (1, 3), (2, 3), (2, 4) }, { (1, 4), (2, 3), (2, 4) }, { (1, 3), (1, 4), (2, 3), (2, 4)}<\/span><\/p>\n

9. Let A and B be two sets such that\u00a0n<\/em>(A) = 3 and\u00a0n<\/em>\u00a0(B) = 2. If (x<\/em>, 1), (y<\/em>, 2), (z<\/em>, 1) are in A \u00d7 B, find A and B, where\u00a0x<\/em>,\u00a0y<\/em>\u00a0and\u00a0z<\/em> are distinct elements.
\n<\/strong>Solution –\u00a0<\/strong>Given, n<\/em>(A) = 3 and\u00a0n<\/em>(B) = 2; and (x<\/em>, 1), (y<\/em>, 2), (z<\/em>, 1) are in A \u00d7 B.
\nWe know that,
\nA = Set of first elements of the ordered pair elements of A \u00d7 B
\nB = Set of second elements of the ordered pair elements of A \u00d7 B
\nSo, clearly,\u00a0x<\/em>,\u00a0y<\/em>, and\u00a0z<\/em> are the elements of A; and
\n1 and 2 are the elements of B.
\nAs\u00a0n<\/em>(A) = 3 and\u00a0n<\/em>(B) = 2, it is clear that set A = {x<\/em>,\u00a0y<\/em>,\u00a0z<\/em>} and set B = {1, 2}<\/span><\/p>\n

10. The Cartesian product A \u00d7 A has 9 elements among which are found (\u20131, 0) and (0, 1). Find the set A and the remaining elements of A \u00d7 A.
\n<\/strong>Solution –\u00a0<\/strong>We know that,
\nIf there are p elements in A and q elements in B, then there will be pq elements in A \u00d7 B, <\/span>
\ni.e., if n(A) = p and n(B) = q, then n(A \u00d7 B) = pq <\/span>
\nGiven, n(A \u00d7 A) = 9 <\/span>
\nSo, n(A) \u00d7 n(A) = 9 <\/span>
\nThus, n(A) = 3 <\/span>
\nAlso given that, the ordered pairs (-1, 0) and (0, 1) are two of the nine elements of A \u00d7 A. <\/span>
\nAnd, we know A \u00d7 A = {(a, a): a \u2208 A}.\u00a0 <\/span>
\nSo, -1, 0, and 1 should be the elements of A.\u00a0 <\/span>
\nAs n(A) = 3, clearly A= {-1, 0, 1}. <\/span>
\nHence, the remaining elements of set A \u00d7 A are as follows: <\/span>
\n(\u20131, \u20131), (\u20131, 1), (0, \u20131), (0, 0), (1, \u20131), (1, 0), and (1, 1)<\/span><\/p>\n

Go Back To Chapters<\/i><\/b><\/a><\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

NCERT Solutions Class 11 Maths\u00a0 The NCERT Solutions in English Language for Class 11 Mathematics Chapter – 2 Relations and Functions Exercise 2.1 has been provided here to help the students in solving the questions from this exercise.\u00a0 Chapter 2 (Relations and Functions)\u00a0 Exercise – 2.1   1. If , find the values of\u00a0x\u00a0and\u00a0y. Solution […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1674],"tags":[1675,1679,1687,1688,1678,1680,1681],"class_list":["post-8384","post","type-post","status-publish","format-standard","hentry","category-class-11-maths","tag-class-11-ncert-mathematics-solutions","tag-class-11-ncert-solutions","tag-ncert-class-11-mathematics-chapter-2-relations-and-functions-solutions","tag-ncert-class-11-mathematics-exercise-2-1-solutions","tag-ncert-class-11-mathematics-solutions","tag-ncert-solutions-class-11-mathematics","tag-ncert-solutions-class-11-maths"],"yoast_head":"\nNCERT Class 11 Maths Solutions - Exercise 2.1 | TheExamPillar NCERT<\/title>\n<meta name=\"description\" content=\"NCERT Solutions Class 11 Maths\u00a0The NCERT Solutions in English Language for Class 11 Mathematics Chapter - 2 Relations and Functions Exercise 2.1 has been provided here to help the students in solving the questions from this exercise.\u00a0Chapter 2 (Relations and Functions)\u00a0\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-11-maths-chapter-2-relations-and-functions-ex-2-1\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"NCERT Solutions Class 11 Maths Chapter 2 Relations and Functions - 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