Question:
A mapping f: R-R which is defined as f(x)=cos x, x ER is
A mapping f: R-R which is defined as f(x)=cos x, x ER is
Updated On: Aug 8, 2024
- one- one only
- onto only
- neither one one nor onto
- one one and onto
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The Correct Option is C
Solution and Explanation
The correct option is(C): neither one one nor onto
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Top Questions on Relations
- A classroom teacher is keen to assess the learning of her students the concept of "relations" taught to them. She writes the following five relations each defined on the set \( A = \{1, 2, 3\} \): \[ R_1 = \{(2, 3), (3, 2)\}, \quad R_2 = \{(1, 2), (1, 3), (3, 2)\}, \quad R_3 = \{(1, 2), (2, 1), (1, 1)\}, \] \[ R_4 = \{(1, 1), (1, 2), (3, 3), (2, 2)\}, \quad R_5 = \{(1, 1), (1, 2), (3, 3), (2, 2), (2, 1), (2, 3), (3, 2)\}. \] The students are asked to answer the following questions about the above relations:
(i) Identify the relation which is reflexive, transitive but not symmetric.
\ (ii) Identify the relation which is reflexive and symmetric but not transitive.
(iii) Identify the relations which are symmetric but neither reflexive nor transitive.
OR
(iii) What pairs should be added to the relation \( R_2 \) to make it an equivalence relation? - Assertion (A): The relation \( R = \{(x, y) : (x + y) \text{ is a prime number and } x, y \in \mathbb{N}\} \) is not a reflexive relation.
Reason (R): The number \( 2n \) is composite for all natural numbers \( n \). - The relation \( R = \{(a, a), (b, b), (c, c), (a, c)\ \) defined on the set \( \{a, b, c\} \) is _____________.}
- Given relation R={(x, y): y=x+5, x < 4, x, y ∈ N}. Where N is a set of natural numbers then :
- Le L be the set of all lines in a plane and R be the relation in L. defined as R = {(\(L_1, L_2\)): \(L_1\) is perpendicular to \(L_2\)} then R is:
A) Reflexive
B) Symmetric
C) Neither reflexive nor transitive
D) Transitive
E) Neither reflexive nor symmetric
Choose the correct answer from the options given below:
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