NCERT Class 12 Maths
Chapter 1: Relations And Functions
16 Questions Solved
NCERT Solutions for Class 12 Maths Chapter 1 Relations And Functions — Exercise 1.1
Click any question below for its step-by-step NCERT textbook solution, concept hints, and worked explanation.
Question 1
Determine reflexivity, symmetry and transitivity for: (i) on A={1,2,…,14}, xRy iff 3x−y=0; (ii) on ℕ={1,2,…}, xRy iff y=x+5 and x<4…
Question 2
On ℝ define aRb iff a≤b². Show that R is neither reflexive nor symmetric nor transitive.
Question 3
On {1,2,3,4,5,6}, define aRb iff b=a+1. Check reflexivity, symmetry and transitivity.
Question 4
On ℝ define aRb iff a≤b. Show that R is reflexive and transitive but not symmetric.
Question 5
On ℝ define aRb iff a≤b³. Check reflexivity, symmetry and transitivity.
Question 6
On A={1,2,3}, R={(1,2),(2,1)}. Show that it is symmetric but neither reflexive nor transitive.
Question 7
On the books in a college library, xRy iff x and y have the same number of pages. Prove that R is an equivalence relation.
Question 8
On A={1,2,3,4,5}, aRb iff |a−b| is even. Prove equivalence and describe the odd and even classes.
Question 9
On A={x∈ℤ:0≤x≤12}, prove equivalence and find the elements related to 1 for (i) |a−b| a multiple of 4; (ii) a=b.
Question 10
Give an example of a relation that is (i) symmetric but neither reflexive nor transitive; (ii) transitive but neither reflexive nor…
Question 11
For points P,Q in a plane, define PRQ iff their distances from the origin are equal. Prove equivalence. For P≠(0,0), describe its…
Question 12
On all triangles, T₁RT₂ iff T₁ is similar to T₂. Prove equivalence. Which of triangles with sides (3,4,5),(5,12,13),(6,8,10) are…
Question 13
On all polygons, P₁RP₂ iff they have the same number of sides. Prove equivalence and describe the class of a right triangle with…
Question 14
On lines in the xy-plane, L₁RL₂ iff they are parallel. Prove equivalence and find all lines related to y=2x+4. Use the textbook…
Question 15
On A={1,2,3,4}, let R={(1,2),(2,2),(1,1),(4,4),(1,3),(3,3),(3,2)}. Choose the correct property description.
Question 16
On ℕ, aRb iff a=b−2 and b>6. Which pair belongs to R?