CBSE Class 12 Mathematics Relations And Functions Worksheet Set 01

CBSE Class 12 Mathematics Relations And Functions Worksheet Set A

MORE QUESTIONS

RELATIONS AND FUNCTIONS

1. Let R be a relation defined as R = { (x,y) : x and y study in the same class}. Show that R is an equivalence relation.

If x is a brilliant student and y is a slow learner and x helps y in his studies, what quality does x possess?

Expected answers:

• Concern about fellow students

• Helping others

• Sharing of knowledge

• Empathy

2. Consider the functions f and g,f: {1, 2, 3} → {a, b, c} and g: {a, b, c} {punctuality, honesty, sincerity} defined as f(1) = a, f(2) = b, f(3) = c, g(a) = punctuality, g(b) = honesty, g(c) = sincerity. Show that f, g, gof are invertible. If a, b, c are three students who are awarded prizes for the three values given in the function g, which value would you prefer to be rewarded and why?

Expected answers: An answer with any of the three values with proper reasoning is correct.

3. Show that the function f : defined by f(x) = 3x + 4 is an invertible function.

If x represents the number of systematic hours of study that a student puts in and f(x) represents the marks scored by him, from the graph of the above function, which value will be rewarded?

Expected answers:

• Systematic study

• Quality of hard work

• Study habit

• Time management

4. Let L be the set of all the lines in a plane and R be the relation in L defined by

R = { L₁,L₂,L₃ | | L₂ }. Show that R is an equivalence relation.

L₁ represents the ideologies of Gandhiji and represents the ideologies of NetajiSubhash Chandra Bose. Even though their ideaologies ran on parallel tracks, both had the common goal to achieve independence for India. Which common value did they both exhibit?

Expected answer:

• Patriotisim

•Sacrifice

• Pride in our country

• Leadership

5. Let Xbe a non-empty set. Let be a binary operation on the power set P(X) defined by A * B = A Ú B . Prove that * is commutative and associative. What is the identity element for the operation *?

If X is a set of people in a locality, A is a set of children and B is a set of citizens aged above 75 years in the same locality, is a * binary operation for these sets as defined above?

What qualities would you suggest that elements of A should have

towards elements of B?

Expected answer:

• Respect for elders

• Concern for the aged

• Lending a helping hand

6. Consider a relation R in the set A of people in a colony. Defined as aRb iff a and b are members of joint family. Is R is an equivalence relation?

VBQ : Staying with Grand parents in a joint family imbibes the moral values in us. Can you elicit 2 such values.

(a) Love and concern for grandparents

(b) Respect for Group parents

(c) Tolerance