Question

part a

. Let A = {1,2,3,4,5},B ={0,3,6} find

1. A∪B

2. A∩B

3. A\B

4. B \ A

Part b

. Show that if A andB are sets,

1. (A\B)⊆A

2. A∪(A∩B)=A

Part c. Determine whether each of these functions from Z to Z is one-to one

1. f(x)=x−1
2. f(x)=x2 +1
3. f(x) = ⌈x/2⌉

Part c. Let S = {−1,0,2,4,7}, find f(S) if

1. f(x)=1
2. f(x)=2x+1
3. f(x) = ⌊x/5⌋

4. f(x)=⌈(x2 +1)/3⌉

Part D. Determine whether each of these functions from Z to Z is onto

1. f(x)=x−1
2. f(x)=x2 +1

3. f(x) = ⌈x/2⌉

part E. Determine whether each of these functions from R to R is a bijection. Find

its inverse function if it is a bijection.

1. f(x)=2x+4
2. f(x)=−x2 −2

3. f(x) = x2 + 2 x2 + 1

Part g Find f ◦g and g◦f, where f(x) = x2 +1 and g(x) = x+2 are functions from R to R.

Answer 1