An immediate answer is neither one of mentioned exams is good for this task ;)
Due to it is supposed to make a complex verification of skills in both areas of expertise. Suggested task 18 veifies ability to identify parametrically set torus definition and understand that it's volume would be (2*PI*R) multiplied by square of rotating circle PI*r^2. Also minimal knowledge of Boolean algebra and sets theory are required to understand task 2 from http://kpolyakov.spb.ru/download/inf-2015-10.pdf
Sets P and Q are defined via parameters in Space R^3
Equation for set Р (torus) looks as follows :-
Equation for set Q looks as follows :-
Please, identify the maximum volume of set A
((X ∈ A) => (X ∈ P))v(X ∈ Q)
which makes logical exression above true for any X ∈ R^3
¬A v P v Q = 1 for all X ∈ R^3
A(max) = PvQ
Answer :-
V(A(max)) =(4/3)PI*(R-r)^3 + (2*(PI)^2)*R*r^2
The torus volume V(P) = (2PI*R)*PI*r^2 and
the volume of sphere with radius (R - r) is
V(Q)=(4/3)*PI*(R-r)^3
Due to it is supposed to make a complex verification of skills in both areas of expertise. Suggested task 18 veifies ability to identify parametrically set torus definition and understand that it's volume would be (2*PI*R) multiplied by square of rotating circle PI*r^2. Also minimal knowledge of Boolean algebra and sets theory are required to understand task 2 from http://kpolyakov.spb.ru/download/inf-2015-10.pdf
Sets P and Q are defined via parameters in Space R^3
Equation for set Р (torus) looks as follows :-
Equation for set Q looks as follows :-
Please, identify the maximum volume of set A
((X ∈ A) => (X ∈ P))v(X ∈ Q)
which makes logical exression above true for any X ∈ R^3
¬A v P v Q = 1 for all X ∈ R^3
A(max) = PvQ
Answer :-
V(A(max)) =(4/3)PI*(R-r)^3 + (2*(PI)^2)*R*r^2
The torus volume V(P) = (2PI*R)*PI*r^2 and
the volume of sphere with radius (R - r) is
V(Q)=(4/3)*PI*(R-r)^3
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