Equivalence Relations and Classes

JEE Main Mathematics · Relations and Functions · 10 questions, latest first

• Consider the relation R on the set {-2,-1,0,1,2} defined by (a, b) ∈ R if and only if 1+ab>0. Then, among the statements: I. The…20268 April, Shift 2 · Q1
• Let A={0,1,2, …, 9}. Let R be a relation on A defined by (x, y) ∈ R if and only if |x-y| is a multiple of 3. Given below are two…202623 January, Shift 2 · Q1
• Let X=R × R. Define a relation R on X as: (a_1, b_1) R(a_2, b_2) ⇔ b_1=b_2. Statement I: R is an equivalence relation. Statement…202523 January, Shift 2 · Q2
• Let R={(1,2),(2,3),(3,3)} be a relation defined on the set {1,2,3,4}. Then the minimum number of elements, needed to be added in…202523 January, Shift 1 · Q2
• The number of non-empty equivalence relations on the set {1,2,3} is:202522 January, Shift 1 · Q2
• Consider the relations R_1 and R_2 defined as a R_1 b ⇔ a^2+b^2=1 for all a, b ∈ R and (a, b) R_2(c, d) ⇔ a+d=b+c for all (a,…20241 February, Shift 2 · Q2
• Let A={1,2,3,4} and R={(1,2),(2,3),(1,4)} be a relation on A. Let S be the equivalence relation on A such that R ⊂ S and the…202431 January, Shift 1 · Q21
• If R is the smallest equivalence relation on the set {1,2,3,4} such that {(1,2),(1,3)} ⊂ R, then the number of elements in R is…202429 January, Shift 2 · Q1
• Let P(S) denote the power set of S={1,2,3, ….., 10}. Define the relations R_1 and R_2 on P(S) as AR_1 B if (A ∩ B^c) ∪(B ∩ A^c)=∅…20231 February, Shift 2 · Q61
• The minimum number of elements that must be added to the relation R={(a, b),(b, c),(b, d)} on the set {a, b, c, d} so that it is…202324 January, Shift 2 · Q81