ASSERTION (A) : The relation f:{1,2,3,4}→{x,y,z,p} defined by f={(1,x),(2,y),(3,z)} is a bijective function.

REASON (R) : The function f:{1,2,3}→{x,y,z,p} such that f={(1,x),(2,y),(3,z)} is one-one.


(a) Both A and R are true and R is the correct explanation of A.

(b) Both A and R are true but R is not the correct explanation of A.

(c) A is true but R is false.

(d) A is false but R is true.

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Checking Assertion ASSERTION (A): The relation 𝑓:{1,2,3,4}→{𝑥,𝑦,𝑧,𝑝} defined by 𝑓={(1,𝑥),(2,𝑦),(3,𝑧)} is a bijective function. Making the diagram for the relation We know that, A relation is a function if every element of first set has an image. In this case element 4 has no image Hence, the given relation is not a function Thus, given relation is not a bijective function So, Assertion is false. Checking Reason REASON (R): The function 𝑓:{1,2,3}→{𝑥,𝑦,𝑧,𝑝} such that 𝑓={(1,𝑥),(2,𝑦),(3,𝑧)} is one-one. Checking one – one 𝑓={(1,𝑥),(2,𝑦),(3,𝑧)} Since each element has a unique image ∴ f is one-one So, reason is true So, Assertion is false Reasoning is true So, the correct answer is (d)

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.