If $$P, Q, R$$ are Boolean variables, then $$\left( {P + \overline Q } \right)$$ $$\left( {P.\overline Q + P.R} \right)\left( {\overline P .\overline R + \overline Q } \right)$$ Simplifies to

In the Karnaugh map shown below, $$X$$ denotes a don’t care term. What is the minimal form of the function represented by the Karnaugh map?

A set of Boolean connectives is functionally complete if all Boolean function can be synthesized using those, Which of the following sets of connectives is NOT functionally complete?

A sample space has two events A and B such that probabilities $$P\,(A\, \cap \,B)\, = \,1/2,\,\,P(\overline A )\, = \,1/3,\,\,P(\overline B )\, = \,1/3$$.
What is P $$P\,(A\, \cup \,B)\,$$?