Activity18- Functions odel III (20min) Inverse Relation. Given a relation R from

Question

Activity18- Functions odel III (20min) Inverse Relation. Given a relation R from A to B, the inverse is a relation R1 from B to A such that (v, x) E R if and only if (x, y) e R1 Example et A -(1, 2, 3, 4, 5) and B - a,b, d). The relation R (1,a),(2.c), (1,d), (3,b)) has inverse R1-{(a, 1), (c,2), (d,1), (b3)). e relation R ((1,a), Explore the model 1. In the model what is the domain of R? The codomain of R? 2. What is the domain of R-1? The codomain? To be a function, a binary relation, R, must have the property that for every element in the domain A, there is exactly one element in the codomain B for which (a, b) is an element of for R. Is the relation in the model a function? 3. Critical Thinking In each case, one of these is a function from A to B and one is not. Circle the one that IS a function Example 1. Let A (1, 2, 3, 4, 5} and B # {1, 2, , 9, 10) 1. a. The relation with the rule {(x,y) e A × B : y = b. The relation with the rule ((x,y) E Ax B:y-2x 2. Example 2. Let A = {1, 2, 3, 4, 5)and B-(1, 2, , 9, 10) a. The relation with the rule ((1,1), (2,3), (4,4), (3,4), (5,6)) b. The relation with the rule ((1,1), (3,2), (4,4), (3,4), (5,6)) ge 7

Explanation / Answer

1. A = {1,2,3,4,5 }

B = {a,b,c,d }

Domain is nothing but what can go into function.

Hence for relation R = {(1,a), (2,c),(1,d),(3,b)}

Therefore Domain of R = {1,2,3}

Codmain is nothing but what may come out of function

Therefore Codomain of R = {a,b,c,d}

2. Domain of inverse of relation R where R-1 = {(a,1),(c,2),(d,1),(b,3)} is:

Domain of R-1 = {a,b,c,d}

Codomain of R-1 = {1,2,3,4,5}

3. No R is not a function. because for element 1 in Domain of R,

there are two possible values, they are a and d

For(A=1) ,B can be a or d. Therefore R is not a function.

Critical thinking

1. A= {1,2,3,4,5} B = {1,2,3,4,5,6,7,8,9,10}

for the relation from A to B to be a function, for each element , there should be only one element in B.

i. for relation where y = x2, for x=5, y should be 25. But B doesn't have the value 25. Likewise for x=4, y=16. There is no 16 in B. Hence the above relation is not a function

ii. for relation y=2*x , for each value x in A there is one value in y in B. Hence this relation is a function.

for x=1, y = 2 => (1,2)

for x=2, y =4 => (2,4)

for x=3, y = 6 =>(3,6)

for x=4, y = 8 =>(4,8)

for x=5, y = 10 =>(5,10)

2.i) Relation from A to B is a function as there is only one value in B for each element in domain A= {1,2,3,4,5} of relation  

ii) Relation form A to B is not a function as for the element '3' in domain A there are two values '2' and '4' in B. Hence it is not a function.

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