Mumbai University > Computer Engineering > Sem 3 > Discrete Structures

Marks: 8 Marks

Year: May 2016

1. (f o g)(1)=f(g(1))=f(2)=3

   (f o g)(2)=f(g(2))=f(1)=2

   (f o g)(3)=f(g(3))=f(3)=1

   f o g={(1,3), (3,1), (2, 2)}

   (g o f)(1)=g(f(1))=g(2)=1

   (g o f)(2)=g(f(2))=g(3)=3

   (g o f)(3)=g(f(3))=g(1)=2

   g o f={(1,1), (2,3), (3, 2)}

   Since from above f o g and g o f are not equal.

2. (f o g o h)(1)=f(g(h(1)))=f(g(1))=f(2)=3

   (f o g o h)(2)=f(g(h(2)))=f(g(2))=f(1)=2

   (f o g o h)(3)=f(g(h(3)))=f(g(1))=f(2)=3

   So, f o g o h={(1, 3), (2, 2), (3, 3)}

3. (f o h o g)(1)=f(h(g(1)))=f(h(2))=f(2)=3

   (f o h o g)(2)=f(h(g(2)))=f(h(1))=f(1)=2

   (f o h o g)(3)=f(h(g(3)))=f(h(3))=f(1)=2

   So, f o h o g={(1, 3), (2, 2), (3, 2)}