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Functions f, g, h are defined on a set, X= {1,2,3} as f= {(1,2) (2,3) (3,1)} g = {(1,2} (2,1) {3,3)) h = {(1, 1 ) (2,2) (3,1)} (i) Find fog, g o f are they equal ? (ii) Find fogoh and fohog.
written 7.8 years ago by gravatar for teamques10 teamques10 ★ 67k modified 2.7 years ago by gravatar for pedsangini276 pedsangini276 • 4.8k

Mumbai University > Computer Engineering > Sem 3 > Discrete Structures

Marks: 8 Marks

Year: May 2016
discrete mathematics
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written 7.8 years ago by gravatar for teamques10 teamques10 ★ 67k

  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 …

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