Q.1 Let f : \{1, 3, 4\}\rightarrow \{1, 2, 5\}and g : \{1, 2, 5\} \rightarrow \{1, 3\} be given by
f = \{(1, 2), (3, 5), (4, 1)\} and g = \{(1, 3), (2, 3), (5, 1)\}. Write down gof.

Answers (1)

Given :       f : \{1, 3, 4\}\rightarrow \{1, 2, 5\}             and       g : \{1, 2, 5\} \rightarrow \{1, 3\}

                  f = \{(1, 2), (3, 5), (4, 1)\}         and      g = \{(1, 3), (2, 3), (5, 1)\}

gof(1) = g(f(1))=g(2) = 3                   \left [ f(1)=2 \, and\, g(2)=3 \right ] 

gof(3) = g(f(3))=g(5) = 1                   \left [ f(3)=5 \, and\, g(5)=1 \right ]

gof(4) = g(f(4))=g(1) = 3                 \left [ f(4)=1 \, and\, g(1)=3 \right ]

Hence,   gof = \left \{ (1,3),(3,1),(4,3) \right \}

 

 

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