Tiêu đề 2.RELATIONS AND FUNCTIONS.pdf ✅

(c.) reflexive but not symmetric and transitive (d.) an equivalence relation (12.) Let R1 and R2 be two relations defined on R by a R1 b ab   0 and 2 aR b a b   . Then, [JEE (Main)-2022] (a.) R1 is an equivalence relation but not R2 (b.) R2 is an equivalence relation but not R1 (c.) Both R1 and R2 are equivalence relations (d.) Neither R1 nor R2 is an equivalence relation (13.) For  N , consider a relation R on N given by R x y x y = + { , : 3 ( )  is a multiple of 7 } . The relation R is an equivalence relation if and only if [JEE (Main)-2022] (a.)  =14 (b.)  is a multiple of 4 (c.) 4 is the remainder when  is divided by 10 (d.) 4 is the remainder when  is divided by 7 (14.) Let R be a relation from the set 1, 2,3, ..,60   to itself such that R a b b pq = = { , : ( ) , where p q, 3  are prime numbers}. Then, the number of elements in R is : [JEE (Main)-2022] (a.) 600 (b.) 660 (c.) 540 (d.) 720 (15.) The relation R a,b : gcd a,b 1,2a b,a,b = =   ( ) ( ) Z is:4 Jan 2023(Evening)] (a.) transitive but not reflexive (b.) symmetric but not transitive (c.) reflexive but not symmetric (d.) neither symmetric nor transitive (16.) The equation     2 x x x x x − + + = 4 3 , where  x denotes the greatest integer function, has: [24 Jan 2023(Evening)] (a.) exactly two solutions in (− , ) (b.) no solution (c.) a unique solution in (−,1) (d.) a unique solution in (− , ) (17.) Let R be a relation on N N defined by (a, b R) (c d, ) if and only if ad b c bc a d ( − = − ) ( ) . Then R is [31 Jan 2023(Morning)] (a.) symmetric but neither reflexive nor transitive (b.) transitive but neither reflexive nor symmetric (c.) reflexive and symmetric but not transitive (d.) symmetric and transitive but not reflexive