List all the bijections from a into b.
a) a={q, r,s} and b={2,3,4}
b) a={1,2,3,4} and b={5,6,7,8}

The list of bijections from A into B are shown below.

Step-by-step explanation:

A function f is called one-to-one or injective, if and only if

for all x and y in the domain of f.

A function f from X to Y is called onto or surjective, if and only if

for every element y∈Y there is an element x∈X with f(x)=y.

If a function is one-one and onto, then it is called bijective.

Part (a):

A={q,r,s} and B={2,3,4}

We need to find all the bijections from A into B.

(1)

(2)

(3)

(4)

(5)

(6)

Part (b):

A={1,2,3,4} and B={5,6,7,8}

We need to find all the bijections from A into B.

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

(13)

(14)

(15)

(16)

(17)

(18)

(19)

(20)

(21)

(22)

(23)

(24)

hope this is what you were asking for!

step-by-step explanation: