The activity-on-arrow network of activities for a construction project is shown in the figure. The durations (expressed in days) of the activities are mentioned below the arrows. The critical duration for this construction project is

A construction project consists of twelve activities. The estimated duration (in days) required to complete each of the activities along with the corresponding network diagram is shown below. Total floats (in days) for the activities 5-7 and 11-12 for the project are, respectively,

Consider the following linear system $$$x+2y-3z=a$$$ $$$2x+3y+3z=b$$$ $$$5x+9y-6z=c$$$
This system is consistent if $$a,b$$ and $$c$$ satisfy the equation

$$X$$ and $$Y$$ are two random independent events. It is known that $$P(X)=0.40$$ and $$\,P\left( {X \cup {Y^C}} \right) = 0.7.$$ Which one of the following is the value of $$P\left( {X \cup Y} \right)$$ $$?$$