1 20 marks total Let X be the set of real numbers Show th.pdf

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adhikaribrothers

1) 20 marks total] Let X be the set of real numbers. Show that the function f:XX defined by f(x)=2x 3 is a. [10 marks] one-to-one function, and also b. [10 marks] onto function. 2) [35 marks total ] Let W={X,Y,Z} and V={c,d}. a. [10 marks] Determine the number of functions from W onto V. b. [30 marks] You may either use drawings like the following to present each distinct function you stated it exists when answered item a. or provide your solution as a set of ordered pairs like f={(a,z),(b,y), (c,z),(d,z)}.

1) 20 marks total] Let X be the set of real numbers. Show that the function f:XX defined by f(x)=2x
3 is a. [10 marks] one-to-one function, and also b. [10 marks] onto function. 2) [35 marks total ] Let
W={X,Y,Z} and V={c,d}. a. [10 marks] Determine the number of functions from W onto V. b. [30
marks] You may either use drawings like the following to present each distinct function you stated
it exists when answered item a. or provide your solution as a set of ordered pairs like f={(a,z),(b,y),
(c,z),(d,z)}

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(1) 7. Find the Order of Growth of the algorithm. Procedure Foo (a1,a2,, an: distinct integers) even :=0 odd :=0; for x:=1 to n for y:=n downto 1 begin sum:=ax+ay if ( sum mod2=0) even := even +1 ; else odd := odd +1 ; end if (even >odd) return even; else return odd; (1) 8. Find the Order of Growth of the Algorithm. Procedure Foo(x: integer; a1,a2,,an : distinct integers) Low :=0; High :=n; mid :=( low + high )/2 while (amid!=x) begin if (x>amid) low := mid; else high := mid -1 ; mid := (low + high )/2 end return mid;.

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