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SHARAM PUBLICATION-RELATIONS AND FUNCTIONS-EXAMPLE
- Let f: X rarr Y If there exists a map g:Y rarr X such that gof = id...
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- Let f:XrarrY. If there exists a map g:YrarrX such that g of=idxand fo ...
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- If ff(x)=cos[pi^2]x+cos[-pi^2]x where [x] stands for the greatest inte...
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- If f:RrarrR,g :RrarrR and h : RrarrR such that f(x)=x^2, g(x)= tan x a...
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- If p is a prime and ab-=0 (mod p) then show that either a=0 (mod p) or...
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- Prove that the relation R on the set Z of all integers defined by R={(...
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- Let n be positive integer and a function f be defined as f(n)={(0 , wh...
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- If f:RrarrR defined by f(x)=5x-8 for all x inR, then show that f is in...
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- Show that the inverse of a bijective function is unique.
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- Show that the inverse of a bijective is also a bijection.
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- Let f={(1,a),(2,b),(3,c),(4,d)} and g={(a,x),(b,x),(c,y),(d,x)} Determ...
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- Prove that the greatest integer function f:R rarr R, given by f(x) = [...
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- Let A and B be sets. Show that f : A xx B rarr B xx A such that f (...
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- Show that the fuction f:RrarrR defined by f (x)=sin x is neither one-...
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- If f:N to N is defined by. f(n)={((n+1)/(2)", if n is odd"),((n)/(2)...
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- Show that a fuction f:RrarrR given by f(x)=ax+b, a, bin R and a!=0 is ...
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- Let* be a binary operation on Q, defined by a*b=(3ab)/(5) .Show that i...
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- If A=N xx N and * is a binary operation on A defined by (a, b) ** (c,...
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- A binary operation * on the set {0,1,2,3,4,5} is defined as a*b= {{...
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- Let us consider a binary operation ** on the set {1, 2, 3, 4, 5} given...
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