Figure P2.1 show 3 systems of 3 components C1, C2,C3. Fig 2.1 (a) in a series sy

Question

Figure P2.1 show 3 systems of 3 components C1, C2,C3.
Fig 2.1 (a) in a series system in which the system isfunctioning only if all 3 components are functioning. Fig 2.1 (b) is a parallel system in which the system isfunctioning as long as at least 1 of 3 components arefunctioning. Fig 2.1 (c) is a "two-out-of-three" system in which the systemis functioning as long as at least 2 components arefunctioning. Let Ak be the event "component k is functioning." Foreach of the 3 system configuratios, express the event "systemis functioning" in terms of the events Ak. Sorry I tried to draw the 2 figures but did not insert mycustom diagram. Please see the Problem 2.15 of Probability, statistics, andrandom processes for electrical engineering by AlbertoLeon-Garcia 3rd edition Figure P2.1 show 3 systems of 3 components C1, C2,C3.
Fig 2.1 (a) in a series system in which the system isfunctioning only if all 3 components are functioning. Fig 2.1 (b) is a parallel system in which the system isfunctioning as long as at least 1 of 3 components arefunctioning. Fig 2.1 (c) is a "two-out-of-three" system in which the systemis functioning as long as at least 2 components arefunctioning. Let Ak be the event "component k is functioning." Foreach of the 3 system configuratios, express the event "systemis functioning" in terms of the events Ak. Sorry I tried to draw the 2 figures but did not insert mycustom diagram. Please see the Problem 2.15 of Probability, statistics, andrandom processes for electrical engineering by AlbertoLeon-Garcia 3rd edition Fig 2.1 (c) is a "two-out-of-three" system in which the systemis functioning as long as at least 2 components arefunctioning. Let Ak be the event "component k is functioning." Foreach of the 3 system configuratios, express the event "systemis functioning" in terms of the events Ak. Sorry I tried to draw the 2 figures but did not insert mycustom diagram. Please see the Problem 2.15 of Probability, statistics, andrandom processes for electrical engineering by AlbertoLeon-Garcia 3rd edition

Explanation / Answer

System b) at least one out of 3 must be functioning = A1 U A2U A3 (U is like an or function in logic)
system c) at least 2 components must be functioning =(A1 A2) U(A2 A3) U(A3 A1) {we need atleast two components to work. Hence combine all possible twocomponents using intersection. and then combine all suchcombinations using union)
Hope it is helpful. Feel free to ask for anyclarifications.

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