question archive These are some sums from relations and functions class 12
These are some sums from relations and functions class 12
Subject:MathPrice: Bought3
These are some sums from relations and functions class 12. Please help me by doing the sums in details with all statements written :
1. Let be the relation on ={1,2,3}given by ={(1,1),(1,2),(2,3),(3,2)}. Determine whether it is reflexive. Write down the smallest collection of ordered pairs to be added to to make it transitive.
2. Consider the set =?∩[−2,2). Write down the number of
a. relations on .
b.reflexive relations on .
3. Give examples (without proof) of
a. a function :?→?such that is injective but not surjective.
b. a function :?→?such that is surjective but not injective.
4. Determine whether the function :?→(0,∞) given by ( )= ^2+1 is onto. Justify your answer.
5. Let and be two sets such that | |=3and | |=4. Write downa.the number of injective functions from to .b.the number of surjective functions from to .
6. Let be a relation on ? given by ={( , ): , ∈?,2 +3 is divisible by 5}. Prove that is an equivalence relation. Find the equivalence class of the element 2∈?.
7. Determine whether the function :?→? given by ( )= x^3/(x^2+1) is bijective or not. Justify your answer.
