# NCERT Solutions for Class 12 Maths Chapter 1 – Exercise 1.1

Here you will get NCERT Solutions for Class 12 Maths Chapter 1 – Exercise 1.1 in the text as well as pdf format. As we all know that NCERT books are very helpful in Class 12 CBSE Board. Here we have given question from Chapter 1 of Class 12th Maths subject along with their respective answers.

NCERT Solutions for Class 12 Maths Chapter 1 Exercise 1.1 Overview | |
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Book | National Council of Educational Research and Training (NCERT) |

Class | 12th Class |

Subject | NCERT Solution Class 12th Maths |

Chapter | Chapter 1 – Relations and Functions |

## Chapter 1: Relations and Functions – Exercise 1.1

**Q-1: Check each and every relation whether the following are symmetric, reflexive and transitive:**

**(i) The relation R of the set S = {2, 3, 4, 5, 6, 7, 8, 9. . . . . . . . 15} is defined as**

**R = {(a, b): 2a – b = 0}**

**(ii) The relation R of the set S having natural numbers is defined as**

**R = {(a, b): b = 2a + 6 and a < 5}**

**(iii) The relation R of the set S = {2, 3, 4, 5, 6, 7} is defined as**

**R = {(a, b): b is divisible by a}**

**(iv) The relation R of the set S having only the integers is defined as**

**R = {(a, b): a – b is an integer}**

**(v) The relation R from the set H having human beings at a particular time in the town is given by:**

**(a) R = {(a, b): a and b is working at the same place}**

**(b) R = {(a, b): a and b are living in the same society}**

**(c) R = {(a, b): a is exactly 6 cm taller than b}**

**(d) R = {(a, b): b is husband of a}**

**(e) R = {(a, b): a is the father of b}**

**Solution:**

**Q-2: Prove that the relation M in the set M of the real numbers which is defined as**

**M = {(x, y): x ≤ y ^{2}} which is neither reflexive, nor transitive, nor symmetric.**

**Solutions**

**Q-3: Check whether the relation given below is reflexive, symmetric and transitive:**

**The relation M is defined in the set {2, 3, 4, 5, 6, 7} as M = {(x, y): y = x + 1}.**

**Solutions:**

**Q-4: Prove that the relation M in M which is defined as M = {(x, y): x ≤ y} is transitive and reflexive, but not symmetric.**

**Solutions**

**Q-5: Check that whether the relation M in M which is defined as M = {(x, y): x ≤ y ^{3}} is transitive, reflexive and symmetric.**

**Solutions**

**Q-6: Prove that the relation M from the set {2, 3, 4} which is given by M = {(2, 3), (3, 2)} is not reflexive nor transitive, but it is symmetric.**

**Solutions**

**Q-7: Prove that the relation M in the set S for all the books in a library of the college BET, the relation given for it is M = {(a, b): a and b have the same number of pages in the book} which is the equivalence relation.**

**Solutions**

**Q-8: Prove that the relation M of the set S = {2, 3, 4, 5, 6} which is given by M = {(x, y): | x – y | is even}, is an equivalence relation. Also, prove that all the elements are related to each other of the set {3, 5} and the elements of (2, 4, 6} are inter- related with each other. But, elements of {3, 5} and {2, 4, 6} are not related to each other nor their any of the elements are interlinked.**

**Solutions**

**Q-9: Prove that all the relation M of the set S = {a ɛ P : 0 ≤ a ≤ 12}, which is given by**

**(a) M = {(x, y): | x – y | is a multiple of 3}**

**(b) M = {(x, y): x = b} is an equivalence relation. Get all the sets of elements which are related to 1 in every case.**

**Solutions**

**Q-10: Give an example for each of the relation, which is**

**(a) Symmetric but, neither transitive nor reflexive.**

**(b) Transitive but, neither reflexive nor symmetric.**

**(c) Symmetric and reflexive but, not transitive.**

**(d) Transitive and reflexive but, not symmetric.**

**(e) Transitive and symmetric but, not reflexive.**

**Solution**

**Q-11: Prove that the relation A in the set S for the points in the plane which is given by A = {(M, N): The distance between the point M from (0, 0) will be the same as the distance between the point N from (0, 0)}, is an equivalence relation. Now, also prove that the set of all the points which is related to the point M ≠ (0, 0) is a circle which is passing from the point P with having centre at origin.**

**Solution**

**Q-12: Prove that the relation A which is defined in the set S for all the triangles as A = {(P _{1}, P_{2}): P_{1}is similar to P_{2}}, is an equivalence relation. Assume three right angled triangles, say, triangle P_{1}having sides 4, 5, 6, triangle P_{2} having sides 6, 14, 15 and triangle P_{3 }having sides 7, 9, 11. Find which triangle among P_{1}, P_{2} and P_{3} will be related?**

**Solutions**

**Q-13: Prove that the relation M is defined in the set S of every polygon in such a way that M = {(R _{1}, R_{2}): R_{1} and R_{2} must have the equal number of sides}, is an equivalence relations. Find all the sets of all the elements in S which is related to the right angled triangle T having sides 4, 5 and 6.**

**Solutions**

**Q-15: Let, M be the given relation in the set S = {2, 3, 4, 5} which is given by-**

**M = {(2, 3), (3, 3), (2, 2), (5, 5), (2, 4), (4, 4), (4, 3)}. Select the correct answer:**

**(a) M is symmetric and reflexive, but it is not transitive.**

**(b) M is transitive and reflexive, but it is not symmetric.**

**(c) M is transitive and symmetric, but it is not reflexive.**

**(d) M is an equivalence relation.**

**Solutions**

**Q-16: Let us consider M be a relation in any set M which is given by**

**M = {(x, y): x = y – 2, y > 6}.**

**Select the correct choice from the following:**

**(a) (2, 4) ɛ M (b) (3, 8) ɛ M**

**(c) (6, 8) ɛ M (d) (8, 7) ɛ M**

**Solutions**