Question

please send correct answers. I will make you as brainalist​

Answer 1

Step-by-step explanation:

Solutions :-

1)

Given that :

n(A) = 4

n(B) = 2

We know that

The total number of relations from A to B if n(A) = m and n(B) = n is 2^mn

We have m = 4 and n = 2

Total number of relations = 2^(4×2)

=> 2⁸

=> 256

2)

Given that :

R ={ (x-1),(x-2) ,x = (2,3,4,5)}

Put x = 2 then (2-1),(2-2) = (1,0)

Put x = 3 then (3-1),(3-2) = (2,1)

Put x = 4 then (4-1),(4-2) = (3,2)

Put x = 5 then (5-1),(5-2) = (4,3)

R = { (1,0),(2,1),(3,2),(4,3)}

Domain = {1,2,3,4}

Range = {0,1,2,3}

3)

Given sets are A = { 2,4,6,8}

and B = {5,7,1,9}

Given relation is R is the relation less from A to B

=> {(2,5),(2,7),(2,9), (4,5),(4,7),(4,9),,(6,7),(6,9),(8,9)}

Domain of R = {2,4,6,8}

Range of R = {1,5,7,9}

4)

Given set A = { 1,2,3}

n(A) = 3

Let the n(B) be n

Total number of relations from A to B = 2^(3×n) =2^3n

According to the given problem

Total relations are = 512

=> 2^3n = 512

=> 2^3n = 2⁹

If bases are equal then exponents must be equal

=> 3n = 9

=>n = 9/3

=> n = 3

So, Number of elements in the set B = 3

5)

Given sets are A = { 1,2,3,4}

and B = N

Let f : A-->B ,f(x) = x² +1

Now Put x = 1 then

=> f(1) = 1²+1 = 1+1 = 2

Now Put x = 2 then

=> f(2) = 2²+1 = 4+1 = 5

Now Put x = 3 then

=> f(3) = 3²+1 = 9+1 = 10

Now Put x = 4 then

=> f(4) = 4²+1 = 16+1 = 17

Range of f(x) = { 2,5,10,17}

Used formulae:-

• Total number of relations from A to B if n(A) = m , n(B) = n is 2^mn

• If bases are equal then exponents must be equal