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P1: Number of one-to-one function from A$\bigotimes A$ is 1.

P2: Function A->B is bijective C->D is bijective then AC and BD is also bijective.

P3: Consider set A,B,C,D then ($A\cup B\cap C\cup D) == (A\cap B\cup C\cap D$)

which of above statement are true and which are false

1 Answer

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Although I have not given this Exam, Still trying.

 

Statement 1- False.

Reason- Number of one one function from set A containing n elements to set B containing m elements is mpn.

ATQ- npn= n!.

Statement 2- True.

Suppose domain and codomain is set of all integers (Z). Then

ATQ- Z^Z -----> Z^Z is same / equivalent to Z ------> Z. [ as integers are closed under multiplication ].

It will be bijective.

 

Statement 3- False.

Counter Example-

A= {1,2}

B= {3,4,1}

C= {1,3,5}

D= {2,5,3}

So, LHS evaluates to {1,2,3}

Ans RHS to  { 1,3,5}.

So LHS # RHS.

FEEL FREE TO CORRECT!

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