Ch - 2 , Relations and functions , Class - 11 , Q- 5,6,7

Sets , Nios, Class-12, Ch-1 ,Ex-1.1 ,Q-1

Which of the following relation are functions? Give reasons. In cane of a function, determine its domain and range. {(1,-2),(3,7),(4,-6),(8,11)}

A function f given as f:{(2,7),(3,4),(7,9),(-1,6),(0,2),(5,3)} . Is this function one-one onto? Interchange the order of the elements in the ordered pairs and form the new relation. Is this relation a function? If it is a function, is it one-one onto.

Let R be the relation defined on the set A={1,\ 2,\ 3,\ 4,\ 5,\ 6,\ 7} by R={(a ,\ b): both a and b are either odd or even}. Show that R is an equivalence relation. Further, show that all the elements of the subset {1, 3, 5, 7} are related to each other and all the elements of the subset {2, 4, 6} are related to each other, but no element of the subset {1, 3, 5, 7} is related to any element of the subset {2, 4, 6}.

Let R be the relation defined on the set A={1,\ 2,\ 3,\ 4,\ 5,\ 6,\ 7} by R={(a ,\ b): both a and b are either odd or even}. Show that R is an equivalence relation. Further, show that all the elements of the subset {1, 3, 5, 7} are related to each other and all the elements of the subset {2, 4, 6} are related to each other, but no element of the subset {1, 3, 5, 7} is related to any element of the subset {2, 4, 6}.

If P=(a,b,c) and Q=(1,2) , then the total number of relations P to Q are not functions is

Examine each of the following relations given below and state in each case, giving reasons whether it is a function or not ? (i) R={(4,1),(5,1),(6,7)} (ii) R={(2,3),(2,5),(3,3),(6,6)} (iii) R={(1,2),(2,3),(3,4),(4,5),(5,6),(6,7)} (iv) R={(1,1),(2,1),(3,1),(4,1),(5,1)}

Let R be a relation such that R = {(1,4), (3,7), (4,5), (4,6), (7,6)} , check R is a function or not ?