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Question 20 [Assertion Reasoning] - CBSE Class 12 Sample Paper for 2024 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at April 16, 2024 by

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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Transcript

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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