Let 𝑆 = {1,2,3, … ,10}. Suppose 𝑀 is the set of all the subsets of 𝑆, then the relation 𝑅 = {(𝐴, 𝐵) : 𝐴 ∩ 𝐵 ≠ 𝜙; 𝐴, 𝐵 ∈ 𝑀} is: Relations (Mathematics) Question | DivineJEE

Let 𝑆 = {1,2,3, … ,10}. Suppose 𝑀 is the set of all the subsets of 𝑆, then the relation 𝑅 = {(𝐴, 𝐵) : 𝐴 ∩ 𝐵 ≠ 𝜙; 𝐴, 𝐵 ∈ 𝑀} is: Relations (Mathematics) Question | DivineJEE | DivineJEE

Let a relation 𝑅 on 𝑁 × 𝑁 be defined as: (𝑥1, 𝑦1)𝑅(𝑥2, 𝑦2) if and only if 𝑥1 ≤ 𝑥2 or 𝑦1 ≤ 𝑦2. Consider the two statements : (I) 𝑅 is reflexive but not symmetric. (II) 𝑅 is transitive Then which one of the following is true?

Let 𝐴 = {1,3,4,6,9} and 𝐵 = {2,4,5,8,10}. Let 𝑅 be a relation defined on 𝐴 × 𝐵 such that 𝑅 = {((𝑎1, 𝑏1), (𝑎2, 𝑏2))∶ 𝑎1 ≤ 𝑏2 and 𝑏1 ≤ 𝑎2}. Then the number of elements in the set 𝑅 is

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 .

Let 𝐴 = {2,3,6,8,9,11} and 𝐵 = {1,4,5,10,15}. Let 𝑅 be a relation on 𝐴 × 𝐵 defined by (𝑎, 𝑏)𝑅(𝑐, 𝑑) if and only if 3𝑎𝑑 − 7𝑏𝑐 is an even integer. Then the relation 𝑅 is

Consider the relations 𝑅1 and 𝑅2 defined as 𝑎𝑅1𝑏 ⇔ 𝑎2 + 𝑏2 = 1 for all 𝑎, 𝑏 ∈ R and (𝑎, 𝑏)𝑅2(𝑐, 𝑑) ⇔ 𝑎 + 𝑑 = 𝑏 + 𝑐 for all (𝑎, 𝑏), (𝑐, 𝑑) ∈ N × N. Then

Let 𝑅 be a relation on 𝑍 × 𝑍 defined by (𝑎, 𝑏)𝑅(𝑐, 𝑑) if and only if 𝑎𝑑 − 𝑏𝑐 is divisible by 5 . Then 𝑅 is

For x ? 0, the least value of K, for which 4^{1 + x} + 4^{1 - x},\frac{K}{2},16^{x} + 16^{- x} are three consecutive terms of an A.P., is equal to :

Let 𝐴 = {1,2,3,4,5,6,7}. Then the relation 𝑅 = {(𝑥, 𝑦) ∈ 𝐴 × 𝐴∶ 𝑥 + 𝑦 = 7} is

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