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Suppose that 120 students are studying i...

Suppose that 120 students are studying in 4 sections of eleventh standard in a school. Let A denotes the set of students and B denote the set of the sections. Define a relation from A to B as "x related to y if the student x belongs to the section y". Is this relation a function ? What can you say about the inverse relation ? Explain your answer.

Answer

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Explore conceptually related problems

Suppose that 120 are studying in 4 sections of eleventh standard in a school. Let A denote the set of students and B denote the set of the sections. Define a relation from A to B as x related to y if the student x belongs to the section y. Is this relation a function? What can you say about the inverse relatioin. Explain your answer.

Let N be the set of natural numbers and the relation R be defined on N such that R={(x,y): y=2x,x,y in N }. what is the domain codomain and range of R ? Is this relation a functions ?

Knowledge Check

  • Let A = { x,y,z } and b= {a,b,c,d}. which one of the following is not relation from A to B ?

    A
    `{(x,a),(x,c)}`
    B
    `{(y,c),(y,d)}`
    C
    `{(z,a),(z,d)}`
    D
    `{(z,b),(y,b),(a,d)}`

  • If A = {1,2,3} , B = {1,4,6,9} and R is a relation from A to B defined by "x is greater than y ". The range of R is

    A
    {1,4,6,9}
    B
    {4,6,9}
    C
    {1}
    D
    none of these.

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    Let A ={1,2,3,4,5,6} . Define a relation R from A to A by R = {(x,y):y =x+1} write down the domain , and range of R .

    Given a non empty set X, consider P (X) which is the set of all subsets of X. Define the relation R in P(X) as follows : For subsets A, B in P(X), ARB if and only if A sub B. Is R an equivalence relation on P (X)? Justify your answer.

    A ={ 1,2,3,5} and B={ 4,6,9 } . Define a relation R from A to B by R = {( x,y) } : the difference between x and y is odd , x in A , y in B } write R in roster form

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    Let A ={1,2,3,4,5,6} . Define a relation R from A to A by R = {(x,y):y =x+1} Depict this relation using an arrow diagram .

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